VI. LEARNING ACTIVITIES: Seatwork #1: Solve the following problems and box your final answers. Patten the step-by-step solution in sample problems. 1.) Write the Maclaurin series form of cos 2x.

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Author:Erwin Kreyszig
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VI.
LEARNING ACTIVITIES:
Seatwork #1: Solve the following problems and box your final answers. Patten the step-by-step solution
in sample problems.
1.) Write the Maclaurin series form of cos 2x.
2.) Write the Taylor series form of e2x at xXg=1.
3.) Use the formula in approximating the derivative (same as Sample Problem 2) of f(x) = 2x – 3x +1
at x=1 using h=0.5. Compute the absolute and relative erors.
4.) What is the greatest value of h that can be used to approximate the derivative of of f(x) = x? at x=4
with an error of no more than 1%?
5.) Determine the relative error when approximating e' using fifth-degree Taylor polynomial with respect
to e" compared to sixth-degree Taylor polynomial.
(Hint: express the degree series using x=-1 to get the exact values)
Transcribed Image Text:VI. LEARNING ACTIVITIES: Seatwork #1: Solve the following problems and box your final answers. Patten the step-by-step solution in sample problems. 1.) Write the Maclaurin series form of cos 2x. 2.) Write the Taylor series form of e2x at xXg=1. 3.) Use the formula in approximating the derivative (same as Sample Problem 2) of f(x) = 2x – 3x +1 at x=1 using h=0.5. Compute the absolute and relative erors. 4.) What is the greatest value of h that can be used to approximate the derivative of of f(x) = x? at x=4 with an error of no more than 1%? 5.) Determine the relative error when approximating e' using fifth-degree Taylor polynomial with respect to e" compared to sixth-degree Taylor polynomial. (Hint: express the degree series using x=-1 to get the exact values)
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