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Single Variable Calculus

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Moderate

Taylor's Theorem

SVCALC-YXL7PQ

Let $f(x)=e^x$ and let $T_2(x)=c_0+c_1x+c_2x^2$ be its second degree Taylor polynomial at $x=0$.

To 3 decimal places, find the number $c$ between $0$ and $2$ guaranteed to exist by Taylor's theorem that satisfies the equation:

$$f(2)-T_2(2)=\frac{f^{(3)}(c)}{3!}2^3$$

This problem requires a calculator.

A

$0.583$

B

$0.840$

C

$1.086$

D

$1.191$

E

$1.606$