By using the standard series, derive the first four non-zero terms of the power series expansion of

Question

By using the standard series, derive the first four non-zero terms of the power series expansion of ${{e}^{2x+1}}\cos 2x$. Write down the range of values of $x$ for the expansion to be valid.

Accepted Answer

$\displaystyle e^{2x+1}\cos2x=e\left(1+2x-\frac83x^3-\frac83x^4+O(x^5)\right)$, valid for all real $x$.

Maclaurin Series and Power Series - Products and Quotients of Power Series

Maclaurin Series and Power Series - Products and Quotients of Power Series

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