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

question 52

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) \(4+4 x+\frac{4 x^{2}}{2}+\frac{4 x^{3}}{3 !}+\frac{4 x^{4}}{4 !}\)

Recognize the importance of optimal emergency services placement for community planning.

Grasp the significance of local optima in optimization problems and their impact on solution quality.

Comprehend the characteristics and applications of nonsmooth models in optimization.

Understand the concept and applications of permutations in optimization problems.

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