Detailed Explanations for Calculus 2 Equations

Find the maximum rate of change of f at the given point and the direction in which it occurs.
$f (x, y, z) = \sqrt{x^{2} + y^{2} + z^{2}}, (9, 7, - 2)$
maximum rate of change =
direction vector =

kerrum75 2021-12-22

Use the comparison or limit comparison test to decide if the following series converge.
$\sum_{n = 1}^{\infty} \frac{4 - \sin n}{2^{n} + 1}$
For each series which converges, give an approximation of its sum, together with an error estimate, as follows. First calculate the sum $s_{5}$ of the first 5 terms, then estimate the "tail" $\sum_{n = 6}^{\infty} a_{n}$ by comparing it with an appropriate improper integral or geometric series.

Jason Yuhas 2021-12-22

I have to find the sine series of $x^{3}$ using the the cosine series of $\frac{x^{2}}{2}$
$\frac{x^{2}}{2} = \frac{l^{2}}{6} + \frac{2 l^{2}}{π^{2}} [\sum \frac{{(- 1)}^{n}}{n^{2}} \cos (\frac{n π x}{l})]$

Mary Reyes 2021-12-22

I have to calculate the series
$\sum_{k = 2}^{\infty} (\frac{1}{k} - \frac{1}{k + 2})$
Using the definition:
$L = lim_{n \to \infty} S_{n} = lim_{n \to \infty} \sum_{k = 0}^{n} a^{k}$
Obviously $lim_{n \to \infty} (\frac{1}{n} - \frac{1}{n + 2}) = 0$ , but I don't think that this is the right way to calculate the value of the series.

Michael Maggard 2021-12-22

Is there a way to rewrite a series like $\sum_{n = 1}^{\infty}$ as a power series? I know its

Bobbie Comstock 2021-12-22

Determined the convergence of this alternating series. The series is $\sum_{i = 1}^{\infty} 2 (\frac{- 1}{4})^{(n - 1)}$

David Lewis 2021-12-21

Evaluate the following integrals. Include absolute values only when needed.
$\int_{0}^{5} 5^{5 x} d x$

Chris Cruz 2021-12-21

Find the indefinite integral.
$\int \csc 2 x d x$

berljivx8 2021-12-20

Find indefinite integral.
$\int - 3 e^{2 x} d x$

eiraszero11cu 2021-12-20

Evaluate the following integrals. Include absolute values only when needed.
$\int \frac{\ln^{2} x + 2 \ln x - 1}{x} d x$

Irvin Dukes 2021-12-20

Evaluate the following integrals.
$\int \frac{e^{x}}{e^{2 x} + 2 e^{x} + 1} d x$

aspifsGak5u 2021-12-20

Find the trigonometric integral.
$\int \frac{\tan^{2} x}{\sec^{3} x} d x$

eiraszero11cu 2021-12-20

Which of the answers is an arithmetic sequence?
a) 2, 4, 8, 16, 32
b) 3, 6, 9, 15, 24
c) 2, 5, 7, 12, 19
d). 6, 13, 20, 27, 34

Linda Seales 2021-12-20

Evaluate the integral.
$\int \cos^{- 6} x d x$

Wanda Kane 2021-12-20

Find two unit vectors orthogonal to both $j - k$ and $i + j$ .

Julia White 2021-12-20

If a curve has the property that the position vector $r (t)$ is always perpendicular to the tangent vector $r^{'} (t)$ , show that the curve lies on a sphere with center the origin.

reproacht3 2021-12-19

Find indefinite integral.
$\int \frac{\sqrt{t}}{2} d t$

Jean Blumer 2021-12-19

Evaluate the integral.
$\int_{0}^{1} \frac{2 \ln (x)}{\sqrt{x}} d x$

socorraob 2021-12-19

Evaluate the integral.
$\int \sec^{2} x \tan x d x$

Juan Hewlett 2021-12-19

Find the indefinite integral.
$\int \frac{e^{\frac{1}{t}}}{t^{2}} d t$

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.

Calculus 2

Calculus 2 Equations: Expert Solutions and More