The Hyperbolic Cosine Function Is Defined as Follows $f(x)=\cosh (x)=\frac{e^{x}+e^{-x}}{2}$ Use the Taylor Polynomial For Defined

Multiple Choice

The hyperbolic cosine function is defined as follows: $f(x) =\cosh (x) =\frac{e^{x}+e^{-x}}{2}$ .Use the Taylor polynomial for $e^{x}$ near 0 to find the Taylor polynomial of degree 4 for $f(x) =4 \cosh (x)$ .

A) $4-\frac{4 x^{2}}{2 !}+\frac{4 x^{3}}{3 !}-\frac{4 x^{4}}{4 !}$
B) $4\left(1+\frac{x^{2}}{2}+\frac{x^{4}}{24}\right)$
C) $4+\frac{3 x}{1 !}-\frac{3 x^{2}}{2 !}+\frac{x^{4}}{24}$
D) $4+4 x+\frac{4 x^{2}}{2}+\frac{4 x^{3}}{3 !}+\frac{4 x^{4}}{4 !}$