15. Power Series

Find the Taylor polynomials of order $0,1,2$, and $3$ for $f\left(x\right)=\ln \left(x\right)$ centered at $x=1$.

Approximate $\sin 0.3$ to four decimal places using the third-degree Maclaurin polynomial for $f\left(x\right)=\sin x$.

Find the interval of convergence for the Taylor series for $f\left(x\right)=\sin x$ centered at $x=\frac{\pi }{2}$.

Find the Taylor Series of $f\left(x\right)=\cos x$ centered $x=\pi$. Then, write the power series using summation notation.

Find the Maclaurin polynomials of order $0,1,2$, and $3$ for $f\left(x\right)=\sin x$

Approximate $\ln 1.5$ to four decimal places using the third-degree Taylor polynomial for $f\left(x\right)=\ln x$.

Find the interval of convergence for the Maclaurin series for $f\left(x\right)={\tan }^{-1}x$