Taylor Series

Practice Questions

AP Calculus BC › Taylor Series

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$\begin{align*}&\text{Approximate }f(1) \&\text{Where }f(x)=- cos(5x) - sin(2x)\&\text{With a Taylor series centered at }\frac{(5\cdot \pi )}{2}\text{, using }3\text{ terms}\end{align*}$

$\begin{align*}&\text{For the function: }f(x)=-cos(4x)^{2}\&\text{Approximate }f(3)\&\text{Using a Taylor expansion centered at }6\cdot \pi\text{ to }2\text{ terms}\end{align*}$

$\begin{align*}&\text{Approximate }f(6) \&\text{Where }f(x)=- cos(9x) - cos(x)\&\text{With a Taylor series centered at }-\frac{(5\cdot \pi )}{2}\text{, using }3\text{ terms}\end{align*}$

$\begin{align*}&\text{For the function: }f(x)=cos(x) +\frac{ 1}{cos(8x)}\&\text{Approximate }f(5)\&\text{Using a Taylor expansion centered at }-4\cdot \pi\text{ to }3\text{ terms}\end{align*}$

$\begin{align*}&\text{Approximate }f(-5) \&\text{Where }f(-2)=-18;f'(-2)=11;f''(-2)=7\&\text{With a Taylor series expansion.}\end{align*}$

$\begin{align*}&\text{Approximate }f(6) \&\text{Where }f(11)=-18;f'(11)=15;f''(11)=5;f'''(11)=-6\&\text{With a Taylor series expansion.}\end{align*}$

$\begin{align*}&\text{Approximate }f(7) \&\text{Where }f(3)=7;f'(3)=16;f''(3)=1\&\text{With a Taylor series expansion.}\end{align*}$

$\begin{align*}&\text{Approximate }f(-7) \&\text{Where }f(-2)=7;f'(-2)=-19;f''(-2)=13;f'''(-2)=10;f''''(-2)=-16\&\text{By using a Taylor expansion.}\end{align*}$

$\begin{align*}&\text{Approximate }f(3) \&\text{Where }f(2)=13;f'(2)=-7;f''(2)=13;f'''(2)=12\&\text{With a Taylor series expansion.}\end{align*}$

$\begin{align*}&\text{For the function values: }\&f(-12)=6;f'(-12)=19;f''(-12)=18;f'''(-12)=-2\&\text{Approximate }f(-10)\text{ using a Taylor expansion.}\end{align*}$

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