ST 552

Calculus on a Computer

Assignment 16 Power Series & Taylor Series

Where do the following converge? Give your reason, and use MAPLE to calculate the value for several x values. Sketch the result.

1.

2.

3.

Find the Taylor’s series for the given function, about the given point. Find the region of convergence. Plot the function and several partial sums of the series on the same graph.

4. about x=0.

5. about x=3.

6. about x=0.

7. about .

8. about x=0 (Think about the derivative.)