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Calculus

Taylor Series

Taylor Series

         

Determine the Taylor series for the function \[f(x) = \sin(x)\cos(x) \text{ centered at } x = \pi.\]

At \( a = 0\), what is the Taylor series expansion of

\[ \ln ( 1 + x ) ? \]

At \( a = 0\), what is the Taylor series expansion of

\[ \frac{1}{(1-x)^2} ? \]

Given the Maclaurin series expansion of \(\exp(x^2)\) as \[a_0 + a_1 x^1 + a_2 x^2 + \cdots ,\] what is the value of \(a_0 + a_1 + a_2 \)?

Determine the first three non-zero terms of the Taylor series for \[f(x) = \tan(x) \text{ centered at } x = \frac{\pi}{4}.\]

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