Problem 3
Use the definition to find the Taylor series (centered at \(c\) ) for the function. $$ f(x)=\cos x, \quad c=\frac{\pi}{4} $$
Problem 3
In Exercises \(3-6,\) find the radius of convergence of the power series. $$ \sum_{n=0}^{\infty}(-1)^{n} \frac{x^{n}}{n+1} $$
Problem 3
Determine the convergence or divergence of the series. $$ \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{n^{2}+1} $$
Problem 3
Find the first five terms of the sequence of partial sums. $$ 3-\frac{9}{2}+\frac{27}{4}-\frac{81}{8}+\frac{243}{16}-\cdots $$
Problem 4
Write the first five terms of the sequence. \(a_{n}=\frac{2 n}{n+3}\)
Problem 4
Find the first five terms of the sequence of partial sums. $$ \frac{1}{1}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\cdot \cdot $$
Problem 4
Use the definition to find the Taylor series (centered at \(c\) ) for the function. $$ f(x)=\sin x, \quad c=\frac{\pi}{4} $$
Problem 4
Use the Integral Test to determine the convergence or divergence of the series. $$ \sum_{n=1}^{\infty} n e^{-n / 2} $$
Problem 4
In Exercises \(3-6,\) find the radius of convergence of the power series. $$ \sum_{n=0}^{\infty}(2 x)^{n} $$
Problem 4
In Exercises \(1-4,\) find a first-degree polynomial function \(P_{1}\) whose value and slope agree with the value and slope of \(f\) at \(x=c .\) Use a graphing utility to graph \(f\) and \(P_{1} .\) What is \(P_{1}\) called? $$ f(x)=\tan x, \quad c=\frac{\pi}{4} $$
