Evaluate the function $f ( x ) = \cos x$ by a Taylor polynomial of degree $4$ centered at $a = 0$ , and $x = \frac { \pi } { 4 }$ .
A) $0.7074$
B) $4.2074$
C) $3.2074$
D) $2.2074$
E) $1.2074$

Question

Quizplus · Accepted Answer

The Taylor polynomial of degree 4 for $f(x) = \cos x$ centered at $a = 0$ is $1 - \frac{x^2}{2} + \frac{x^4}{24}$. Evaluating this at $x = \frac{\pi}{4}$ gives approximately $0.7074$.

Evaluate the Function f(x)=cos⁡xf ( x ) = \cos xf(x)=cosx By a Taylor Polynomial of Degree

Evaluate the Function $f ( x ) = \cos x$ By a Taylor Polynomial of Degree