Use the Taylor Series For $f(x)=\cos (x)$ At X = 0 to Find the Taylor Series For 0

question 39

Multiple Choice

Use the Taylor series for $f(x) =\cos (x)$ at x = 0 to find the Taylor series for $\cos (\sqrt{x})$ at x = 0.

• A) \(1-x+\frac{x^{2}}{2 !}-\frac{x^{3}}{3 !}+\cdots\)
• B) \(1-\frac{x}{2 !}+\frac{x^{2}}{4 !}-\frac{x^{3}}{6 !}+\cdots\)
• C) \(\sqrt{x}-\frac{x}{2 !}+\frac{x^{3 / 2}}{4 !}-\frac{x^{2}}{6 !}+\cdots\)
• D) \(\sqrt{x}-x+\frac{x^{3 / 2}}{2 !}-\frac{x^{2}}{3 !}+\cdots\)

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