Calculus
Which of the following could be the interval of convergence for the power series ∑ck(x−4)k\(\sum\) c_{k}(x-4)^{k}?
Express m(z)=z51−z m(z) = \(\frac{z^5}{1-z}\) as a power series centered at 00. What is its interval of convergence?
Find the radius RR and interval of convergence for the power series ∑n=1∞y6nn2{\(\displaystyle\]\sum\)_{n=1}^{\(\infty\)}\(\frac{y^{6n}\)}{n^2}} using the Ratio Test.
Evaluate the following limit using Taylor series: limy→0tan3yy\(\displaystyle{\lim_{y \to 0}\)} \(\frac{\tan 3y}{y}\)
Find the second-order Taylor polynomial for f(x)=sin−1xf(x)=\(\sin\)^{-1}x centered at a=12a=\(\frac\)12.
Find the radius and interval of convergence for the power series:
∑n=1∞(4y−1)nn \(\displaystyle\) \(\sum\)_{n=1}^{\(\infty\)} \(\frac{(4y - 1)^n}{n}\)
