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Taylor Series

The Taylor series is a polynomial of infinite degree used to represent functions like sine, cube roots, and the exponential function. They're how some calculators (and Physicists) make approximations.

Taylor Series Manipulation

         

Determine the Taylor series for the function

\[f(x)=\sinh x ~\text{ centered at }~ x=0.\]

Determine the Taylor series for the function

\[f(x)=\cosh x ~\text{ centered at }~ x=0.\]

Determine the Taylor series for the function

\[f(x)=e^{x^2} ~\text{ centered at }~ x=0.\]

Determine the Taylor series for the function

\[f(x)=\frac{1}{(1 - x)^2} ~\text{ centered at }~ x=0 ~\text{ for }~ \left |x \right |<1.\]

Determine the Taylor series for the function

\[f(x)=\sin{x^2} ~\text{ centered at }~ x=0.\]

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