50g Basics
By Eddie Shore
(Last Revised 10/8/2007)
Introduction: Here in this section, we will show an efficient way to get answers on the 50g. I will start with the basics and then the advanced functions. Remember, there usually is more than one way to do a task! This guide is aimed for the beginning users who are using the 50g for the first time.
Setting RPN Mode:
Press MODE, then [+/-] until operating mode says "RPN". Then press ENTER.
I will be using the RPN in all examples. There is a learning curve involved, but the benefits are:
1. You calculate the way you think.
2. You get immediate results, which can guide you through the problems.
3. (Almost) No parenthesis are required!
4. It is often faster to do calculations in RPN.
Arithmetic.
Addition: y ENTER x +
Subtraction: y ENTER x -
Multiplication: y ENTER x X (I will use * to denote multiplication.
Division: y ENTER x ÷
Example 1: (8 + 2) * (16 ÷ 4) - 2
Press: 8 ENTER 2 + 16 ENTER 4 ÷ * 2 -
Answer: 38
Example 2: 2 + 3 * (6 ÷ 9)
11 - 5
Tip: In problems like this, conquer the numerator, then denominator, then divide to get your answer.
Press: 2 ENTER 3 ENTER 6 ENTER 9 ÷ * + (Numerator: 2 + 3 * 2/3 or 4)
11 ENTER 5 -| (Denominator: 6)
Â÷ EVAL (Answer: 2/3 or .6666...)
Scientific Notation
Power of 10:
1. Enter mantissa.
2. Press EEX
3. Enter power - between -499 to +499
Example 3: Enter -3.6089 x 10^23.
Press: 3.6089 +/- EEX 23 ENTER
Display will show -3.6089E23 (E in this case stands for "10^")
Reciprocal Key 1/X
Divides 1 by whatever is in Level 1. Make sure that 0 is not in Level 1 or you will get an error message or infinity (depending your flag settings).
Example 4: 1/2 + 1/3 + 1/4 + 1/5 Convert the answer into approximation (numerical) form.
Press: 2 1/X 3 1/x + 4 1/X + 5 1/X + RS ->NUM
Answer: 1.2833 (rounded to 4 places)
Note:
LS = Left Shift, on the 50g it is the White key with the arrow pointing up and left
RS = Right Shift, on the 50g it is the Orange key with the arrow pointing up and right
To force a numerical answer, RS ->NUM (ENTER Key)
Clearing the Stack
Use the command CLEAR.
Press: RS CLEAR (Backspace Key)
That's it! We will review other stack commands later.
Powers and Roots
Power: y (base) ENTER x (power) Y^X
Root: y (base) ENTER x (power) RS xy| (it is supposed to "look" like a universal root
I will refer to this function as XROOT
Square Root of x: x SQRT
I will refer to this function as SQRT
Square of x: x LS x^2
Example 5:
| (3 + 8) * (3 * 8) | 2
| ---------------------- + 6 | x 3.24 = 2,022.6375...
| SQRT(2) |
Big expression to calculate. But with the beauty of RPN, you get to break the problem down in parts. I tend to go from left to right.
Press: Checkpoints:
3 ENTER 8 ENTER + 3 ENTER 8 * (You should have 11 on Level 2 (y); 24 on Level 1 (x) at this point)
* 2 SQRT ÷ (Level 1 should read 264/SQRT(2) or 186.6761...)
6 + 3.24 LS x^2 * (Level 1 now reads (264/SQRT(2) + 6) * 10.4976 or 2022.6375...)
EVAL (2022.6375...)
(If you are in Exact mode, almost any time you introduce a number with a decimal point, the 50g will ask you to switch to Approximate mode)
Example 6: Take the 4/3rd root of 8. We will use the XROOT and Power functions to do this problem.
Press: 8 ENTER 4 Y^X (Level one should read 4096)
3 RS XROOT (Final answer: 16)
Logarithmic and Exponential Functions
Base 10 - Shifted functions on the EEX key
Common Logarithm: RS LOG
Common Antilogarithm: LS 10^x
Base e - Shifted functions on the Y^X key
Natural Logarithm: RS LN
Natural Antilogarithm: LS e^x
Example 7: We can use the common logarithm to determine the number of digits of an integer by the formula INT(LOG n) + 1 where INT is the integer function.
The integer function, named the IP (Integer Part) function in the 50g, can be found in this manner, LS MATH, Real..., IP. For those who use soft menus: LS MATH, F5 (REAL), NXT, F5 (IP)
Set the calculator to Soft Menus, type -117, SF (Type 1, 1, 7, +/-, ALPHA, S, ALPHA F, ENTER). SF stands for Set Flag. I will be using the soft menus in all future examples.
Now onto to Example 7 ("Get along with it already!"): find the number of digits in 42,544,283,102,392,384,992.
Press: 42544283102392384992 RS LOG LS MATH F5 (REAL) NXT F5 (IP) 1 +
Answer: 20
Example 8: Demonstrate that ln (x) + ln (y) = ln (x * y) is true with a numerical example: Let x = 1.89 and y = 2.64.
Press:
1.89 RS LN 2.64 RS LN + (Level 1 should have 1.6073...)
1.89 ENTER 2.64 * LN (Both levels 1 and 2 should have 1.6073.... now for the comparison test...)
LS PRG F4 (TEST) F1 (==) (Level 1 should show 1. (true)
Example 9: 10^e
Press:
1 LS e^x LS 10^x
Answer: ALOG(e^1), or pressing RS ->NUM gives 522.7352...
Trigonometric Functions and Angle Settings
The first indicator on the top row is the angle setting: DEG for Degrees, RAD for Radians, GRD for Gradients.
You need to know what type of angle units you are working with before you operate with trigonometric functions. Degrees are often used in geometry, while calculus and higher math (and graphing) dictate that you work with Radians. Gradients are a European measure.
360 degrees = 2 * pi radians = 400 gradients
One way to set the angle mode is to press MODE, Down Arrow twice to Angle Measure..., and finally F2 (CHOOS) to select the angle mode.
A faster way, just type DEG for Degree Mode, RAD for Radian Mode, and GRAD for Gradient Mode, then press ENTER.
Now the trig functions:
Sine: SIN
Cosine: COS
Tangent: TAN
Arcsine (sin^-1): LS ASIN
Arccosine (cos^-1): LS ACOS
Arctangent (tan^-1): LS ATAN
Example 10: The famous triangle problem...
Press:
MODE, scroll to Angle Measure and select Degrees, ENTER twice. Alternatively, type "DEG" (ALPHA D, ALPHA E, ALPHA G) and press ENTER.
30 SIN 10 * EVAL (Level 1 shows 5, the value of x)
30 COS 10 * EVAL (Level 1 shows 5 * SQRT(3), the value of y. The numerical approximation is 8.6602...)
Example 11: Find the angle (theta) in degrees and radians.
Press:
3 ENTER 4 Â÷ LS ATAN RS ->NUM shows approximately 36.8699 degrees.
Converting angels from Degrees to Radians (and back and regardless of angle setting):
Press LS MTH F5 (REAL) NXT NXT and then...
F4 (D->R) to convert Degrees to Radians and
F5 (R->D) to convert Radians to Degrees
Example 12: Convert 90 degrees to radians and then pi/6 to degrees.
Press: 90 LS LS MTH F5 (REAL) NXT NXTF4 (D->R) to get an approximate of 1.5708 Radians.
LS 
(SPC Key) 6 ÷ F5 (R->D) to get 30 degrees.
Conquering the Percent Key
To get the percent (%) function, press LS MTH F5 (REAL) F1 (%)
The percent key takes to arguments: the "whole" number on Level 2 and the percent (not decimal form) on Level 1. We think use of this key is best illustrated by this example.
Example 13: What is 70% of 500?
Press: 500 ENTER 70 LS MTH F5 (REAL) F1 (%) RS ->NUM. The answer should be 350.
Example 14: You buy several items at the store. One is pair of pants, normally priced at $36.99, but has a 20% discount, a blouse for $18.99, having a 10% discount, and a watch for $35.99 with 15% off that price tag. Assume each item is taxable and 8.25% sales tax applies. How much better be in your account by the time you reach the check register?
Press:
LS MATH F5 (REAL) (Going to the menu where the % is found.)
36.99 ENTER ENTER 20 F1 (%) - (To add or subtract percentages, you must duplicate a number on both Levels 1 and 2.)
18.99 ENTER ENTER 10 F1 (%) - +|
35.99 ENTER ENTER 15 F1 (%) - +
EVAL (at this point, the hard work is done)
The final bill is $83.65.
The Stack
The stack is a storage area where immediate results are stored. I have been referring the stacks as "levels". Level 1 is the most immediate level, meaning any unary operation (i.e. SIN, LN, EXP (e^x), ABS, etc) will have an immediate affect on the contents of Level 1.
Commonly, level 1 is referred to as the "X"-Register. You will notice on the SQRT key has X to show that the operation acts on the "X" register. Please note that the key X puts the variable X on the stack.
Level 2 is referred to as the "Y"-Register.
When you enter an object, be a number, or more advanced objects like algebraic expressions, matrices, lists, and programs, the object is place on Level 1 while everything else "goes up" one level. Unlike most non-graphing RPN calculators, the 50g (as well as the 48 and 49 series) has an unlimited amount of levels. That is, you can have as many immediate results you want, as long you have memory.
When a binary calculation is executed (among others, +, -, *, ÷, Y^X, XROOT) the calculation takes place with the contents of Levels 2 (Y) and Level 1 (X) and puts the result in Level 1. Everything else "moves down" one level.
Now some stack simple stack operations:
Clear the Entire Stack: Press RS CLEAR (Backspace key). This just clears the entire stack. Alternatively, you can press TOOL and then F6 (CLEAR) to do the same thing.
Swap the contents of Level 2 and Level 1: Similar to the exchange key (x<>y) you find on the non-graphing RPN calculators.
If you are on the home screen (check the screens of the last example), just press the -> (right arrow) to swap. Otherwise, press LS PRG F1 (STACK) F2 (SWAP).
Finally, you can press TOOL F3 (STACK) F2 (SWAP). Note that when you are programming, the Stack Menu gets bumped a page when pressing TOOL.
Roll the contents of the Stack: On the 50g, you must specify how many levels do you want to "roll". Pressing 3 ROLL, rolls 3 levels up, regardless of how many levels are present. Pressing 3 ROLLD, rolls 3 levels down.
If you want the entire stack to roll, you should execute the DEPTH command first, and then execute the ROLL or ROLLD command. The command sequence DEPTH ROLLD is similar to the R(down arrow) key on the non-graphing RPN calculators.
DEPTH: Either LS PRG F1 (STACK) or TOOL F3 (STACK) and then NXT F6 (DEPTH)
ROLL (Up): Either LS PRG F1 (STACK) or TOOL F3 (STACK) and then NXT F1 (ROLL)
ROLL (Down): Either LS PRG F1 (STACK) or TOOL F3 (STACK) and then NXT F2 (ROLLD)
Pick a level: Say you want an immediate result to work with, but that result is stacked on a high level. No problem, just pick the level you want, and use the PICK command. The contents are placed on Level 1 while everything else is moved up a level.
PICK: Either LS PRG F1 (STACK) or TOOL F3 (STACK) and then NXT F3 (ROT)
Drop: You can erase the contents of Level 1 and bring everything else down a level by using the DROP command.
DROP: Either LS PRG F1 (STACK) or TOOL F3 (STACK) and then F3 (DROP). Alternatively, when something isn't being entered, use Backspace key.
Other Stack operations include:
Rotate: Use ROT and UNROT to "rotate" the first three levels of the stack. F5 (ROT) and F6 (UNROT) once you get to the Stack Menu.
ROT: Whatever is in Level 3 goes to Level 1, Level 2 goes to Level 3, and Level 1 goes to Level 2. (same as 3 ROLL)
UNROT: Whatever is in Level 3 goes to Level 2, Level 2 to Level 1, and Level 1 to Level 3. (same as 3 ROLLD)
Copy Over: F4 (OVER) once you get to the Stack Menu.
Copies whatever is in Level 2 and puts it as Level 1 - while moving everything else up. (same as 2 PICK)
Duplicate, Duplicate Twice, Duplicate Two Items:
From the Stack Menu:
DUP: F1 (DUP) to duplicate whatever is on Level 1. Everything else moves up one level.
DUPDUP: NXT NXT F5 (DUPDU) makes two copies of the contents of Level 1. Everything else moves up two levels.
DUP2: NXT NXT F1 (DUP2) makes a copy of Level 2 and Level 1, in that order. Everything else moves up two levels.
There are many other stack operations, each are described in the 49g+ Advanced User Reference. Unfortunately, the stack operations are not described in the User's Manual.
Common Math Operations and How to Get There
Here I highlight some of the common math operations (and some of my personal favorites). Learn more in the HP 50g User's Guide, Chapters 3 and Appendix J.
Some Common Numeric Functions - MATHS REAL Menu: LS MTH F5 (REAL)
F1 (%) - Percent operation, see Conquering the Percent Key section above
F2 (%CH) - Percent Change; find the percent change between Y and X. Level 2 represents the old and Level 1 represents the new.
Example 15: The price of a vintage calculator sold for $395 when first released in 1979. Today, one in mint condition sells for $450. What is the percent change? Give a numeric answer.
Press: 395 ENTER 450 LS MTH F5 (REAL) F2 (%CH) RS ->NUM
The calculator appreciated approximately 13.9241%.
F5 (MOD) - Modulo. Gives the remainder of the division of two integers. Remainder(y ÷ x).
Example 16: What is the remainder of 110 ÷ 8?
Press: 110 ENTER 8 LS MTH F5 (REAL) F5 (MOD)
The remainder is 6.
F1 (ABS) (on the second page, get there by pressing NXT) - Absolute Value. Returns the -(x) when x < 0, otherwise returns x.
Alternatively, you can press LS ABS (÷ key).
Also (featured) on Page 2 of the MATHS-REAL Menu:
F2 (SIGN) - The Sign function. Returns -1 if the number is negative, 0 if the number is 0, and 1 if the number is positive.
F3 (MANT) - Returns the mantissa (as if the number would have been written in scientific notation)
F4 (XPON) - Returns the exponent of a number (as if the number would have been written in scientific notation)
F5 (IP) - Returns the integer part of a number
F6 (FP) - Returns the fraction part of a number
Example 17: Return the integer and fraction parts of 1788/969. Add the two to get the decimal approximation of 1788/969.
Press:
Method 1: (Use the keyboard for DUP and SWAP)
1788 ENTER 969 ÷ (Level 1 should show 596/323 or 1.8452...)
ENTER (to duplicate Level 1)
LS MTH F5 (REAL) NEXT F5 (IP) (Level 1 should show 1. IP returns the answer in approximate format)
right arrow (swaps Levels 1 and 2)
F6 (FP) (Level 1 should show .8452...)
+ (Done! Level 1 should show 1.8452...)
Method 2: (Use the Stack operations - I will use the PRG - STACK route - but you can use the TOOL - STACK route)
1788 ENTER 969 ÷ (Level 1 should show 596/323 or 1.8452...)
LS PRG F1 (STACK) F1 (DUP) (to duplicate Level 1)
LS MTH F5 (REAL) NEXT F5 (IP) (Level 1 should show 1.)
LS PRG F1 (STACK) F2 (SWAP) (swaps Levels 1 and 2)
LS MTH F5 (REAL) NEXT F6 (FP) (Level 1 should show .8452...)
+ (Done! Level 1 should show 1.8452...)
Some Common Probability Functions - MATHS PROB menu, LS MTH NXT F1 (PROB)
F1 (COMB) - Combination - nCr where n is on Level 2 and r is on Level 1. Use this to find the number of possible arrangements where order is NOT important. COMB answers this question: How many ways can I arrange r objects from a set of n objects, and I don't care about the order?
F2 (PERM) - Permutation - nPr where n is on Level 2 and r is on Level 1. This is where the order of each arrangement IS important. PERM answers this question: How many ways can I arrange r objects from a set of n objects, and the order in which the r objects are arranged is important to me.
Example 18: John is trying to figure the odds of getting various hands in a standard game of poker. Assuming the deck has no jokers, how many possible 5-cards can John be dealt? We assume order is not important, so COMB is the correct function.
Press: 52 ENTER 5 LS MTH NXT F1 (PROB) F1 (COMB)
Answer: 2598960. There are 2,598,960 possible poker hands in a standard deck of playing cards.
Example 19: Stacy, a programmer, wants to create a program on how to arrange a set of blocks colored red, blue, black, yellow, white, green, pink, brown, sky blue, sea green, magenta, violet, gold, and gray (that's 14 colors) into 8 color sequences. Here is order is important, so we use the PERM function.
Press: 14 ENTER 8 LS MTH NXT F1 (PROB) F2 (PERM)
Answer: 121080960. There are 121,080,960 possible codes. Hope Stacy does not plan to input all sequences by hand.
F3 (!) - Factorial. Returns x! = x * (x-1) * (x-2) *... * 1
The neat thing is that the Factorial function can accept all real numbers.
Gamma Function, part 1: Gamma(x) = (x -1)!
Example 20: Joanna wants to arrange 35 place settings for her formal reception. How many ways can she do it?
Press: 35 ALPHA RS 2 ENTER
Returns: 10333147966386144929666651337523200000000 or approximately 1.0333 x 10^40 arrangements. Joanna has options, more than she could possibly want.
F4 (RAND) - returns a random number between 0 and 1. No inputs required.
(on 2nd Page - get there by NXT)
F3 (UPTN) - Upper tail Normal Distribution Probability between x and positive infinity. Inputs: Mean on Level 3, Variance on Level 2, and x-Point on Level 1. To use the standard Normal Curve, let Mean = 0 and Variance = 1.
Hyperbolic Functions - MATHS HYP Menu LS MTH F4 (HYP)
F1 (SINH) - Hyperbolic Sine
F2 (ASINH) - Inverse Hyperbolic Sine
F3 (COSH) - Hyperbolic Cosine
F4 (ACOSH) - Inverse Hyperbolic Cosine
F5 (TANH) - Hyperbolic Tangent
F6 (ATANH) - Inverse Hyperbolic Tangent
Exact and Approximate Modes
Exact Mode: numbers are expressed as rational numbers, fractions. Also, pi and roots are displayed the textbook. The calculator displays an "=" to indicate Exact Mode.
Approximate Mode: numbers are expressed as approximations. The calculator displays an "~" to indicate Approximate Mode.
It is easy to toggle between the two modes. First, HOLD RS down while pressing ENTER.
You can display numbers in exact number and approximate numbers regardless of mode by using two conversion functions.
->NUM converts any number into an approximation.
Key strokes: RS ->NUM
XQ converts any number into an exact amount. XQ must either be typed or found in the Catalog (RS CAT (SYMB key))
Key strokes: X ALPHA Q ENTER
Example: Display sin(/4) as an exact value and an approximation. Set the calculator into Radians.
Press: ALPHA R ALPHA A ALPHA D (if needed - the calculator displays RAD on the top line of the screen)
| LS |
|
|
4 |
÷ |
|
SIN |
X ALPHA Q ENTER (Level 1 should display SQRT(2)/2 - the exact value)
RS ->NUM (Now it displays .707106781185)
Fix Format
To limit the number of decimal places a number shows, there are two ways to do it. One is through the MODE Menu (by the MODE key). The other is to key LS PRG NXT F4 (MODES) F1 (FMT) type in a number from 0 - 12 F2 (FIX)
To turn the calculator into floating point mode, set the Decimal Format to STD (Standard).
From here on out, I will have the calculator in FIX 4 mode for all approximations.
Algebraic Expressions and CAS
Here I will provide a short introduction to algebraic expressions and some calculus.
To start entering an algebraic expression, with, or without a variable, that can be operated on mathematically. Enter all algebraic expressions first by pressing the ' key (which is just under the NXT key). Here, you are going to enter stuff algebraically. Fear not, parenthesis are provided by pressing LS ( ) (- key).
Algebraic expressions that are entered must be surrounded by single quotes. The calculator provides both when you press ' . The calculator provides both sides the parenthesis when entered. Sometimes you must use the right arrow to "escape" nested parenthesis. It takes a little practice.
Let us practice entering algebraic expressions first.
A side note: the Equation Writer, accessed by RS EQW is an excellent way to enter algebraic expressions and equations. See Chapter 2 of the User's Guide (the short book) for a good treatment on the Equation Writer, starting on page 2-5).
Example 21: Enter the following expressions: (Realize you can do this to using the RPN and stack, but we will enter these as algebraic objects)
1. Key: ' 2 * SIN 3 * X ENTER
2. Key: ' SQRT LS ( ) 2 Y^X 2 - 3 Y^X X ENTER
3. Key: ' LS e^X +/- LS ( ) X ÷ 2 right arrow right arrow Â÷ LS ENTER
4. Key: ' 2 * LS ( ) X - 2 right arrow * LS ( ) X - 3 right arrow Y^X 3 ÷ LS ( ) X + 1 ENTER
The next example is use of fractions. You can use separate algebraic expressions to enter fractions and mixed numbers and use RPN to do calculations.
Example 22: Calculate 1/2 + 2 3/4 ÷ 6/7
Press: ' 1 ÷ 2 ENTER (Level 1 should show 1/2)
' 2 + 3 ÷ 4 ENTER (Level 1 should show 2 + 3/4)
+ (Level 1 displays 1/2 + 2 + 3/4)
' 6 ÷ 7 ENTER ÷ (Level 1 displays (1/2 + 2 + 3/4)/(6/7))
EVAL (Get the final answer of 91/24.)
LS ARITH (4 key) NXT F2 (PROPF) (Display the fraction as proper: 3 + 19/24)
The SYMB Key - Symbolic Menu
The SYMB key will be one of your best friends. It has access to the common advanced CAS commands plus quick solving tools. I will use this key throughout the next batch of examples.
Algebra and Calculus
Expand an algebraic expression by the EXPAND command. Reduce it into its factors by using the FACTOR command. Both commands are found in many places.
Example 23: Expand (X + 2)^3.
Method 1: (Algebraic Expression)
Press: ' LS ( ) X + 2 right arrow Y^X 3 ENTER SYMB F1 (ALG) F1 (EXPAN)
Method 2: (RPN way)
Press: X ENTER 2 + 3 Y^X SYMB F1 (ALG) F1 (EXAPN)
Both methods will yield X^3 + 6*X^2 + 12*X + 8
Example 24: Factor X^3 + 3*X^2 - 4
Method 1: (Algebraic Expression)
Press: ' X Y^X 3 + 3 * X Y^X 2 - 4 ENTER SYMB F1 (ALG) F2 (FACTO)
Method 2: (RPN way)
Press: X ENTER 3 Y^X 3 ENTER X ENTER 2 Y^X * + 4 - SYMB F1 (ALG) F2 (FACTO)
Both methods will yield (X-1)*(X+2)^2
From here on out, you choose the method of entering expressions that works best for you. I will only tell you what to put on the stack. If you have trouble with keystrokes regarding entering expressions, please let me know at ews773@hotmail.com.
Substitution
The SUBST command works like substitutes of value (or even another expression) for any variable. Key: SYMB F1 (ALG) F4 (SUBST)
The format: Level 2 is the an expression and on Level 1 an expression in the form of variable for a value to be substituted=value
Example 25: For the expression SQRT(A^2 + B^2), substitute A=3, then substitute B=4.
1. Key the expression 'SQRT(A^2+B^2)' on to the stack. (i.e. ALPHA A ENTER 2 Y^X ALPHA B ENTER Y^X + SQRT)
2. Key in the required substitution; Press ' ALPHA A RS = 3 ENTER
3. Execute the SUBT command: SYMB F1 (ALG) F4 (SUBST)
At this point, Level 1 should show SQRT(3^2 + B^2). Now substitute for B=4.
1. Key ' ALPHA B RS = 4 ENTER
2. Key SYMB F1 (ALG) F4 (SUBST)
Level 1 now should show SQRT(3^2 + 4^2). Evaluate it to get the answer.
1. Key EVAL. The answer of course, is 5.
Sums
Now we start calculating sums of expressions, where X is the index, A is the beginning point, B is the ending point, and F(X) represents an expression of F in X.
The general RPN setup for sums is:
Level 4: X (or index variable)
Level 3: A (beginning point)
Level 2: B (ending point)
Level 1: F(X) (expression)
Key: RS SIGMA (SIN key - by the way, SIGMA is shown as the capital Greek letter sigma)
Example 26: The Zeta Function is defined for real numbers as
Estimate Zeta(2) by calculating the sum of 1/X^2 to 250 terms.
Setup:
Level 4: X
Level 3: 1
Level 2: 250
Level 1: '1/X^2'
Level 1 displays 1.6409 to 4 decimal places (which is correct to 2 decimal places, Zeta(2) is actually 1.6429...)
Derivative
There are many commands to do derivatives on the HP 50g. Here, I show just one of them.
The general set up is:
Level 2: F(X) (expression)
Level 1: X (variable)
RS delta (TAN key - on the keyboard it is symbolized by the small Greek letter delta.)
Example 27: Find the derivative with respect to X to X^2 + 3*X -1.
Method 1:
Setup:
Level 2: 'X^2+3*X-1' (expression)
Level 1: X (variable)
Level 1 yields the answer 2*X+3.
Note: If you are taking the derivative with respect to X, you can use the DERVX command, found by pressing SYMB F3 (CALC) F2 (DERVX). All you need is F(X) on Level 1.
Integral
There are many commands to do integrals on the HP 50g. Here, I show just one of them.
The general set up is:
Level 4: A (lower limit)
Level 3: B (upper limit)
Level 2: F(X) (algebraic expression)
Level 1: X (variable to be integrated on)
Key: RS Integral (TAN key, the function is symbolized like an elongated "S")
Example 28: Find the area under the curve for the function F(X) = sin X from 0 to 
. Be sure you are in radians mode before you start.
Setup:
Level 4: 0
Level 3:
Level 2: 'SIN(X)'
Level 1: 'X'
Level 1 shows the area under the curve, 2.
Example 29: Sometimes you can use a symbolic object (X, T, etc) to execute anitderivatives. Find the antiderivative of F'(X) = X^2 - 6
Method 1:
Setup:
Level 4: 0 (be aware about the lower limit you choose, sometimes you may want to choose 1E-15, especially if F'(X) is undefined at 0)
Level 3: 'X'
Level 2: 'T^2-6'
Level 1: 'T'
Level 1 shows the antiderivative (with c=0): (X^3 - 18*X)/3
Method 2: Use the INTVX command. Put the expression on Level 1, then press SYMB F3 (CALC) F4 (INTVX)
Setup: 'X^2-6' on Level 1
| SYMB |
|
F3 (CALC) |
|
F4 (INTVX) |
You get the same answer as the previous method.
Solve for X
Again, here is one of the many ways the calculator can be used to solve for a variable. In this method, we solve for X in F(X).
The command is SOLVEVX (the VX is hidden). How to find it: SYMB F5 (SOLVE) F4 (SOLVE) (the first "SOLVE"). All you need is F(X) on Level 1. F(X) must be an equation containing X. That is, F(X) must have sign of equality (i.e. =, >, <, etc)
Example 30: Solve for X: X^2 - 7*X = 1.
Level 1: 'X^2-7*X=1'
| SYMB |
|
F5 (SOLVE) |
|
F4 (SOLVE) |
Level 1 will show {X=(-7+SQRT(53))/2 X=(7+SQRT(53))/2}
Complex Numbers
To enter Complex Numbers in Rectangular form, (a + bi). Two ways:
Method 1: ' a + b * LS i ENTER
Method 2: LS ( ) a SPC b ENTER
Example 31: Calculate (3 + 7i)/(2- 7i). I will use Method 1 for this example.
Press: ' 3 + 7 * LS i ENTER (Level 1 shows 3 + 7*i Using Method 2 would yield (3, 7))
' 2 - 7 * LS i ENTER ÷ EVAL (Turn Complex Mode on if asked)
Level 1 returns -(43-35*i)/35 (or if you used Method 2, (-0.8113, 0.6604) to found decimal places)
To enter Complex Numbers is Polar form, (a angle b); Enter:
| LS |
|
( ) |
a |
SPC |
|
ALPHA |
|
RS |
6 b |
ENTER |
Depending on what mode you are in the complex number will be displayed in rectangular or polar mode.
Switching between Rectangular and Polar Modes: Press MODE and choose Coord System.
Example 32: Calculate (5 angle 60 degrees) * (2 angle 30 degrees).
First, use the MODE key to set the calculator in Degrees mode (Angle Measure) and Polar mode (Coord System).
Next, key LS 5 SPC ALPHA RS 6 60 ENTER (Level 1 should show (5, angle symbol 60 degrees)
| LS |
2 |
SPC |
|
ALPHA |
|
RS |
6 30 |
ENTER |
|
* |
The answer is (10 angle 90 degrees)
Common Complex Functions
Accessible from the MATHS COMPLEX Menu, reached by LS MTH NXT F3 (CMPLX)
(Among Others)
First page:
F1 (RE) - Returns the real part of a complex number (Rectangular format)
F2 (IM) - Returns the imaginary part of a complex number (Rectangular format)
F5 (ABS), also LS ABS (÷ key) - The magnitude of a complex number
F6 (ARG), also LS ARG - The argument (angle) of a complex number
Second page:
F3 (CONJ) - Returns the conjugate of a complex number
Example 33: Convert 7.33 - 9.56i to Polar Coordinates. Leave angle in Degrees.
Press: ' 7.33 - 9.56 * LS i ENTER ENTER (Enter the number twice)
LS MTH NXT F3 (CMPLX) F5 (ABS) (Level 1 shows the magnitude: 12.0467 to 4 places)
right arrow (Swap) F6 (ARG) RS ->NUM (Level 1 now shows the angle: -52.5213 to 4 places)
So 7.33 - 9.56i is (12.0467, angle -52.5213 degrees)
Example 34: Convert (4.5, angle 36 degrees) to Rectangular Coordinates.
Press: LS ( ) 4.5 SPC ALPHA RS 6 36 ENTER ENTER
LS MTH NXT F3 (CMPLX) F1 (RE) (Level 1 shows the real part: 3.6406 to 4 places)
right arrow (Swap) F2 (IM) (Level 1 now shows the imaginary part: 2.6450 to 4 places)
So (4.5, 36 degrees) is 3.6406 + 2.6450
Entering Complex Numbers in Polar format involving .
If you try to enter the constant pi as an angle the regular way, you get a Syntax Error. You must enter its numerical equivalent.
Common numerical constants involving :
| pi/4 |
.785398163398 |
| pi/3 |
1.0471975512 |
| pi/2 |
1.5707963268 |
| pi |
3.14159265359 |
| 2*pi |
6.28318530718 |
Next time: matrices, lists, and graphing.
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