Calculus

Taylor Series

Taylor Series - Problem Solving

         

Determine the Taylor series for the function

f(x)=01sinxxdx  centered at  x=0.f(x)=\int _0 ^1 \dfrac{\sin x}{x}dx ~\text{ centered at }~ x=0.

Evaluate π22!π44!+π66!π88!+.\frac{\pi^2}{2!}-\frac{\pi^4}{4!}+\frac{\pi^6}{6!}-\frac{\pi^8}{8!}+\cdots.

Determine the Taylor series for the function

f(x)=sinxcosx  centered at  x=0.f(x)=\sin x\cos x ~\text{ centered at }~ x=0.

Evaluate

n=1(1)n+1n2n. \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \cdot 2^n }.

If f(x)=ex2f(x)=e^{x^2}, what is f(2016)(0)f^{(2016)}(0) ?

×

Problem Loading...

Note Loading...

Set Loading...