1. Write the 3rd degree Taylor polynomial, T, (x), for f(x) = e", centered at 0. (Do this using the Maclaurin series for e'). Your polynomial should have four terms.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Write the 3rd degree Taylor polynomial, T, (x), for f(x) = e", centered at 0. (Do this using the
Maclaurin series for e"). Your polynomial should have four terms.
2. Use your Taylor polynomial to calculate T, (0.5). Round to four decimal places. Compare your
answer to your calculator's value for e05 How far off is your Taylor polynomial?
3. Estimate the remainder R, (0.5). Notice 0s zs 0.5. Since f4) (z) = e s e05 < 2,
use 2 for f"(z). Round to four decimal places.
Transcribed Image Text:1. Write the 3rd degree Taylor polynomial, T, (x), for f(x) = e", centered at 0. (Do this using the Maclaurin series for e"). Your polynomial should have four terms. 2. Use your Taylor polynomial to calculate T, (0.5). Round to four decimal places. Compare your answer to your calculator's value for e05 How far off is your Taylor polynomial? 3. Estimate the remainder R, (0.5). Notice 0s zs 0.5. Since f4) (z) = e s e05 < 2, use 2 for f"(z). Round to four decimal places.
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