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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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