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Let f (x) = 2x cos(2x) − (x − 2)2 and x0 = 0.
a. Find the third Taylor polynomial P3(x), and use it to approximate f (0.4).
b. Use the error formula in Taylor s Theorem to find an upper bound for the error |f (0.4) −P3 (0.4)|. Compute the actual error.
c. Find the fourth Taylor polynomial P4(x), and use it to approximate f (0.4).
d. Use the error formula in Taylor s Theorem to find an upper bound for the error |f (0.4) − P4 (0.4)|. Compute the actual error. |
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