# Calculus 2 questions and answers

Recent questions in Calculus 2
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CoormaBak9 2020-10-28

### Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series. $f\left(x\right)=\mathrm{ln}\sqrt{4-x}$

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Maiclubk 2020-10-27

### Which of the series, and which diverge? Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.) $\sum _{n=1}^{\mathrm{\infty }}\frac{3}{\sqrt{n}}$

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Amari Flowers 2020-10-27

### Find the interval of convergence of the power series. $\sum _{n=1}^{\mathrm{\infty }}\frac{\left(-1{\right)}^{n}{x}^{n}}{n}$

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slaggingV 2020-10-26

### Expand $\frac{1}{\sqrt[4]{1+x}}$ as a power series

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slaggingV 2020-10-26

### For each of the following series, using no tests besides the nth Term and Comparison Tests, determine whether the series converges, diverges to $±\mathrm{\infty }$, or diverges, not to $±\mathrm{\infty }$ $\sum \frac{n-1}{{n}^{2}-1}$

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Josalynn 2020-10-26

### Discuss the convergence of the following series: $\sum _{n=1}^{\mathrm{\infty }}\frac{\mathrm{cos}n\pi }{{n}^{2}+1}$

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generals336 2020-10-25

### Determine whether the given series is convergent or divergent. Explain your answer. If the series is convergent, find its sum. $\sum _{n=0}^{\mathrm{\infty }}\frac{{3}^{n}+{2}^{n+1}}{{4}^{n}}$

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sibuzwaW 2020-10-25

### Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series. $\sum _{n=2}^{\mathrm{\infty }}\frac{\left(-1{\right)}^{n}n}{{n}^{2}-3}$

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Marvin Mccormick 2020-10-25

### Find the sum of the convergent series. $\sum _{n=1}^{\mathrm{\infty }}\frac{1}{9{n}^{2}+3n-2}$

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Cem Hayes 2020-10-23

### Use the Integral Test to determine whether the infinite series is convergent. $\sum _{n=1}^{\mathrm{\infty }}\frac{5}{{4}^{\mathrm{ln}n}}$

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texelaare 2020-10-23

### Identify a convergence test for the following series. If necessary, explain how to simplify or rewrite the series before applying the convergence test. You do not need to carry out the convergence test. $\sum _{k=3}^{\mathrm{\infty }}\frac{2{k}^{2}}{{k}^{2}-k-2}$

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jernplate8 2020-10-23

### Radius and interval of convergence Determine the radius and interval of convergence of the following power series. $x-\frac{{x}^{3}}{4}+\frac{{x}^{5}}{9}-\frac{{x}^{7}}{16}+...$

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floymdiT 2020-10-23

### Use the Limit Comparison Test to determine the convergence or divergence of the series. $\sum _{n=1}^{\mathrm{\infty }}\frac{1}{{n}^{2}\left({n}^{2}+4\right)}$

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Bergen 2020-10-21

### Representing functions by power series Identify the functions represented by the following power series. $\sum _{k=1}^{\mathrm{\infty }}\frac{{x}^{2k}}{k}$

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Rivka Thorpe 2020-10-21

### Find the Maclaurin series for the function. (Use the table of power series for elementary functions.) $f\left(x\right)=\frac{{e}^{{x}^{4}}}{4}$

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foass77W 2020-10-20

### Use the formula for the sum of a geometric series to find the sum. $\sum _{n=4}^{\mathrm{\infty }}\left(-\frac{4}{9}{\right)}^{n}$

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ka1leE 2020-10-20

### Show that the series converges. What is the value of the series? $\sum _{n=2}^{\mathrm{\infty }}\left(-\frac{5}{3}{\right)}^{n}\left(\frac{2}{5}{\right)}^{n+1}$

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Khadija Wells 2020-10-19

### a) Find the Maclaurin series for the function $f\left(x\right)=\frac{1}{1}+x$ b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function $g\left(x\right)=\frac{1}{\left(x+1{\right)}^{2}}$ c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function $h\left(x\right)=\frac{1}{\left(x+1{\right)}^{3}}$ d) Find the sum of the series $\sum _{n=3}^{\mathrm{\infty }}\frac{n\left(n-1\right)}{2n}$ This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is $\frac{7}{2}$

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lwfrgin 2020-10-19

### Determine if the following series converge. If the series converges, calculate its value. Justify your answer. $\sum _{n=1}^{\mathrm{\infty }}\frac{{n}^{2}}{n!\left(\mathrm{log}\left(2\right){\right)}^{n}}$

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Wierzycaz 2020-10-19

### Determine if the series converges or diverges. If the series converges find its sum $\sum _{n=1}^{\mathrm{\infty }}\frac{6}{\left(4n-1\right)\left(4n+3\right)}$

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.