# TI-84 Programs

### Newton's Method

PROGRAM:NEWTON
1. :Input "X0:",A
2. :Input "N:",N
3. :For(B,1,N)
4. :A-Y1(A)/nDeriv(Y1,X,A)→A
5. :Disp A
6. :End

### Average Value

PROGRAM:AVEVAL
1. :Input "A:",A
2. :Input "B:",B
3. :Disp fnInt(Y1,X,A,B)/(B-A)

### Slope of a Polar Function

PROGRAM:PolarS
1. :Input "θ:",θ
2. :nDeriv(r1,θ,θ)→D
3. :(Dsin(θ)+r1cos(θ))/(Dcos(θ)-r1sin(θ))→S
4. :Disp S

### Left Riemann Sum

PROGRAM:LEFTSUM
1. :Input "A:",A
2. :Input "B:",B
3. :Input "N:",N
4. :(B-A)/N→W
5. :0→S
6. :For(C,0,N-1)
7. :WY1(A+C*W)+S→S
8. :End
9. :Disp S

### Right Riemann Sum

PROGRAM:RIGHTSUM
1. :Input "A:",A
2. :Input "B:",B
3. :Input "N:",N
4. :(B-A)/N→W
5. :0→S
6. :For(C,1,N)
7. :WY1(A+C*W)+S→S
8. :End
9. :Disp S

### Middle Riemann Sum

PROGRAM:MIDSUM
1. :Input "A:",A
2. :Input "B:",B
3. :Input "N:",N
4. :(B-A)/N→W
5. :0→S
6. :For(C,0.5,N)
7. :WY1(A+C*W)+S→S
8. :End
9. :Disp S

### Trapezoidal Sum

PROGRAM:TRAPSUM
1. :Input "A:",A
2. :Input "B:",B
3. :Input "N:",N
4. :(B-A)/N→W
5. :0→S
6. :For(C,0,N-1)
7. :W/2(Y1(A+C*W)+Y1(A+C*W+W))+S→S
8. :End
9. :Disp S

### Simpson's Rule Sum

PROGRAM:SIMPSUM
1. :Input "A:",A
2. :Input "B:",B
3. :Input "N:",N
4. :(B-A)/N→W
5. :0→S
6. :For(C,0,N-1)
7. :W/3(Y1(A+C*W)+Y1(A+C*W+W))+S→S
8. :End
9. :For(C,1,N-1,2)
10. :2W/3Y1(A+C*W)+S→S
11. :End
12. :Disp S

### Taylor Series Formula

PROGRAM:TAYLOR
1. :P(X)=F(A)+F'(A)(X-A)+F"(A)(X-A)2/2+F"'(A)(X-A)3/3!+

## TI-84 Functions

Function Where can I find it? What does it do?
θ X,T,θ,n Simply the independent variable of a polar function. Make sure to put your calculator in polar mode by pressing MODE+POL
Input PRGM+I/O+1 Displays text then accepts input for a variable such as A.
For( PRGM+4 Repeats the code between For( and End while setting the first variable to values in the provided range.
Y1 VARS+Y-VARS+1 Accesses the function labeled Y1.
r1 VARS+Y-VARS+3 Accesses the function labeled r1.
nDeriv( MATH+8 Approximates the derivative of a function at a value.
fnInt( MATH+9 Approximates the antiderivative of a function at a value
Disp PRGM+8 Displays a number or variable on the screen.
STO> Stores a number or text inside of a variable.