Question

Find the MacLauren series representation for \( h(x)=x \cdot \cos (2 x) \). \( h(x)=-1+x-\frac{4 x^{3}}{2!}+\frac{16 x^{3}}{4!}-\frac{64 x^{2}}{6!}+\ldots \) \( h(x)=x-\frac{4 x^{3}}{2!}+\frac{16 x^{5}}{4!}-\frac{64 x^{7}}{6!}+\ldots \) \( h(x)=1-x+\frac{4 x^{3}}{2!}-\frac{16 x^{5}}{4!}+\frac{64 x^{7}}{6!}-\ldots \) \( h(x)=x-\frac{4 x^{3}}{3!}+\frac{16 x^{5}}{5!}-\frac{64 x^{7}}{7!}+\ldots \) \( h(x)=x+\frac{4 x^{3}}{2!}+\frac{16 x^{5}}{4!}+\frac{64 x^{7}}{6!}+\ldots \)

          Find the MacLauren series representation for \( h(x)=x \cdot \cos (2 x) \).
\( h(x)=-1+x-\frac{4 x^{3}}{2!}+\frac{16 x^{3}}{4!}-\frac{64 x^{2}}{6!}+\ldots \)
\( h(x)=x-\frac{4 x^{3}}{2!}+\frac{16 x^{5}}{4!}-\frac{64 x^{7}}{6!}+\ldots \)
\( h(x)=1-x+\frac{4 x^{3}}{2!}-\frac{16 x^{5}}{4!}+\frac{64 x^{7}}{6!}-\ldots \)
\( h(x)=x-\frac{4 x^{3}}{3!}+\frac{16 x^{5}}{5!}-\frac{64 x^{7}}{7!}+\ldots \)
\( h(x)=x+\frac{4 x^{3}}{2!}+\frac{16 x^{5}}{4!}+\frac{64 x^{7}}{6!}+\ldots \)

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Find the MacLauren series representation for h(x)=x ·cos (2 x).
h(x)=-1+x-(4 x^3)/(2!)+(16 x^3)/(4!)-(64 x^2)/(6!)+…
h(x)=x-(4 x^3)/(2!)+(16 x^5)/(4!)-(64 x^7)/(6!)+…
h(x)=1-x+(4 x^3)/(2!)-(16 x^5)/(4!)+(64 x^7)/(6!)-…
h(x)=x-(4 x^3)/(3!)+(16 x^5)/(5!)-(64 x^7)/(7!)+…
h(x)=x+(4 x^3)/(2!)+(16 x^5)/(4!)+(64 x^7)/(6!)+…

Added by Sara R.

Calculus

Ron Larson, Robert P. Hostetler, Bruce… 8th Edition

Chapter 9

Instant Answer

Solved by Expert Drew Scalzo

Step 1

Step 1: Recall the Maclaurin series for \( \cos(x) \): \[ \cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots \] Show more…

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Find the MacLauren series representation for \( h(x)=x \cdot \cos (2 x) \). \( h(x)=-1+x-\frac{4 x^{3}}{2!}+\frac{16 x^{3}}{4!}-\frac{64 x^{2}}{6!}+\ldots \) \( h(x)=x-\frac{4 x^{3}}{2!}+\frac{16 x^{5}}{4!}-\frac{64 x^{7}}{6!}+\ldots \) \( h(x)=1-x+\frac{4 x^{3}}{2!}-\frac{16 x^{5}}{4!}+\frac{64 x^{7}}{6!}-\ldots \) \( h(x)=x-\frac{4 x^{3}}{3!}+\frac{16 x^{5}}{5!}-\frac{64 x^{7}}{7!}+\ldots \) \( h(x)=x+\frac{4 x^{3}}{2!}+\frac{16 x^{5}}{4!}+\frac{64 x^{7}}{6!}+\ldots \)

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