Use worksheet **Taylor Polynomials
and Taylor Series **to solve Problem 1.

**Problem
1. ** Consider the function

(b) Plot them together with the graph of g(x) on the interval
[-1, 1].

Use worksheet **Fourier
Polynomials and Series **to solve Problem 2.

**
Problem 2 ** Consider the function g(x)
=
for x between
and
repeated periodically.

(a) Compute and have Maple print the Fourier polynomials of degrees 5,7, and 11.

(b) Plot them together with the graph of g(x) on the interval [- , ] .

Use worksheet **Differential
Equations **to solve Problem 3.

*dy/dx =** y **x/(1 + x*^{2}) *+ y*^{2} ,* y(1) = 2.*

**Problem
3. ** Consider the following ODE

*dy/dx = y **x/(1 + x ^{2})
*

(a) Find the general solution to the equation.

(b) Plot the slope field corresponding to the equation for x and y between -2 and 2.

(c) Solve the initial value problems