Calculus I:  Mathematica Introduction

Using Mathematica to Do Things

Clear[f,g,h]

Use Mathematica to perform the following tasks.

Problem 1

Evaluate cos(π/9) to 12 decimals of accuracy.

Problem 2

Factor 816 (x^2)-58 (x^3)+(x^4)+10 x y-(y^2)

Problem 3

Multiply out the quantity (((1+b))^34).

Problem 4

Plot the function f(x)=(x/((x^2)+1)).

Your plot should look like this:

Problem 5

Plot the implicit function x+y=sin x tan y, for -2≤x≤2 and -2≤y≤2.

Problem 6

Plot the function y=sin(x)-cos(x) as a dashed, thick, purple line.

Problem 7

Define the piecewise defined function

f(x) = (Piecewise[{{x, x<23}, {-sin(x), x≥23}}])

Then, plot f(x).

Problem 8

Plot the three functions on the same set of axes: f(t)=t, g(t)=sin t, h(t)=(Sqrt[t])

Problem 9

Find the roots of f(x)=3(x^4)+(x^2)-1. Verify the roots you find make f zero. Hint: Define f(x), use Solve, then copy/paste to evaluate f at the roots. You may need to use Simplify to verify the roots make f zero.

Problem 10

Find f∘g when f(x)=cos x and g(x)  = arcsin x. What is the value of (g ∘f)(2) ?

Syntax Checks

Clear[f,g,h]

The following Mathematica commands have syntax errors. Fix the errors so the commands will work.

Problem 1

plot[x^2,(x,-2,2)]

Problem 2

h[x]=Exp[x]
h[1]

Problem 3

a=0.1
g[x]=(3x-4)/(ax)
Plot[g[x],{x,1,3}]

Problem 4

Solve[3x^2-4x=2,x]

Problem 5

f[x_]=e^{-3x}
Plot[f[x],{x,-2,2}]

Problem 6

f[t_]=Log[t^2]
Solve[f[x]==3,t]