Maclaurin Series

Practice Questions

AP Calculus BC › Maclaurin Series

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For which of the following functions can the Maclaurin series representation be expressed in four or fewer non-zero terms?

$\begin{align*}&\text{Approximate }f(-4) \&\text{Where }f(0)=-12;f'(0)=-10;f''(0)=16;f'''(0)=8\&\text{By using a Maclaurin expansion.}\end{align*}$

$\begin{align*}&\text{For the function values: }\&f(0)=-8;f'(0)=11;f''(0)=8\&\text{Approximate }f(2)\text{ using a Maclaurin expansion.}\end{align*}$

$\begin{align*}&\text{Approximate }f(3) \&\text{Where }f(x)=-cos(5x)e^{(-3x)}\&\text{With a Taylor series centered at zero, using }3\text{ terms}\end{align*}$

$\begin{align*}&\text{Approximate }f(2.1) \&\text{Where }f(x)=-sin(3x)sin(7x)\&\text{By using a Maclaurin expansion to }3\text{ terms}\end{align*}$

Write out the first three terms of the Taylor series about for the following function:

$\begin{align*}&\text{Approximate }f(1.2) \&\text{Where }f(x)=-cos(x)\&\text{By using a Maclaurin expansion to }3\text{ terms}\end{align*}$

Find the Taylor series expansion of $\frac{1}{1-x^{2}}$ at .

$\begin{align*}&\text{Approximate }f(-8) \&\text{Where }f(0)=-20;f'(0)=-3;f''(0)=6\&\text{With a Maclaurin series expansion.}\end{align*}$

$\begin{align*}&\text{Approximate }f(3) \&\text{Where }f(0)=18;f'(0)=-13;f''(0)=-10\&\text{With a Maclaurin series expansion.}\end{align*}$

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