Show that the series1 x2!+ x24! x36! +is the Maclaurin series for the functionf(x) =cos
Chapter 9, Problem 53(choose chapter or problem)
Show that the series
\(1-\frac{x}{2 !}+\frac{x^{2}}{4 !}-\frac{x^{3}}{6 !}+\cdots\)
is the Maclaurin series for the function
\(f(x)=\left\{\begin{array}{l}\cos \sqrt{x}, x \geq 0 \\\cosh \sqrt{-x}, x<0\end{array}\right.\)
[Hint: Use the Maclaurin series for \(cos x\) and \(\cosh x\) to obtain series for \(\cos \sqrt{x}\), where \(x \geq 0\), and \(\cosh \sqrt{-x}\), where \(x \leq 0\).]
Equation Transcription:
{
Text Transcription:
1 − x/ 2! + x^2/4! − x^3/6! +· · ·
f(x) = {cos sqrt x, x ≥ 0 cosh sqrt −x, x < 0
cos x
cosh x
cos sqrt x
x > or = 0
cosh sqrt −x
x < or = 0
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