Read sections 8.11, 10.1, 10.2, and 10.3 of the text (Thomas/Finney).

• Maple work on taylor polynomials. First, work through the maple worksheet I provided to make sure that you understand what I did.
  
  
  • Consider f(x) = 1/x. 1) Find the first five Taylor polynomials when you expand about x=1. 2) Consider the interval [1/3,5/3]. Plot each Taylor polynomial versus f on this interval. Discuss what you observe. 3) Now find the error bounds E_0, E_1, E_2, E_3, and E_4 for the interval [1/3,5/3] and plot the errors to demonstrate that they respect the error bounds. Demonstrate that if you look at the errors on a larger interval then they can violate the error bounds.
    
    
  • Consider f(x) = sin(x). 1) Find the first nine Taylor polynomials when you expand about x=0. 2) Consider the interval [-5,5]. Plot the following Taylor polynomials versus f on this interval: p_0, p_1, p_2, p_3, p_4, p_5, p_7, p_9. Discuss what you observe. 3) Now find the error bounds E_0, E_1, E_3, E_5, E_7, and E_9 for the interval [-5,5] and plot the errors to demonstrate that they respect the error bounds. Demonstrate that if you look at the errors on a larger interval then they can violate the error bounds.
    
    
  • Consider f(x) = x^2 exp(-x). 1) Find the first five Taylor polynomials when you expand about x=2. 2) Consider the interval [1,3]. Plot each Taylor polynomial versus f on this interval. Discuss what you observe. 3) Now find the error bounds E_0, E_1, E_2, E_3, and E_4 for the interval [1,3] and plot the errors to demonstrate that they respect the error bounds. Demonstrate that if you look at the errors on a larger interval then they can violate the error bounds.
    
    

• section 8.11: 4, 12, 44, 52

• section 10.1: 9, 16, 20, 28, 30, 38

• section 10.2: 11, 16, 28, 42, 53

• section 10.3: 8, 16, 20, 25, 32, 45, 52

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Here's a sample maple worksheet for you to look at for help.

Problems with Maple? Here are the commands I used.

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For one extra point on the homework, print out and use the homework cover sheet. This is a *.pdf document that you print and staple to the front of your homework.

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