Detailed Explanations for Calculus 2 Equations

Solving summation $2 n + 2^{2} (n - 1) + 2^{3} (n - 2) + . . . . + 2^{n}$

pighead73283r 2022-11-09

Evaluate the Sum $\sum_{i = 0}^{\infty} \frac{i^{N}}{4^{i}}$

Kyler Oconnor 2022-11-09

For any positive integer n , let $\hat{n}$ denote the integer nearest to $\sqrt{n}$ . Then how to prove that
$\sum_{m = 1}^{\infty} \frac{2^{\hat{m}} + 2^{- \hat{m}}}{2^{m}} = 3$

Jonas Huff 2022-11-09

Absolute convergence of the series $\sum_{n = 1}^{\infty} (- 1)^{n} \ln (\cos (\frac{1}{n}))$

Hallie Stanton 2022-11-08

Let $a_{n} = \sqrt[n]{n} - 1$ . Does $\sum_{n = 1}^{\infty} a_{n}$ converge?

deal4markaz 2022-11-07

Q: State And Prove Rolles Theorem With Diagram?

bucstar11n0h 2022-11-07

Does the sequence defined by
$x_{n} = (\sqrt[n]{e} - 1) \cdot n$ converge?

Alvin Parks 2022-11-07

Find: $\sum_{n = 0}^{\infty} {(\frac{1}{1 + 3 \cdot (- 1)^{n}})}^{n}$

kemecryncqe9 2022-11-07

Evaluation of $\sum_{n = 1}^{\infty} \frac{2 n - 1}{2^{n}}$

MMDCCC50m 2022-11-06

The square of the sum of three consecutive numbers is 225. What are the numbers.

Barrett Osborn 2022-11-06

$x \log (x) + y \log (y) = 1$
$\frac{d y}{d x} = ?$
I calculated $\frac{d y}{d x} = - \frac{1 + \log (x)}{1 + \log (y)}$
however, the correct answer seems to be $- \log (x) / \log (y)$
I'm confused, can someone help?

Emmanuel Giles 2022-11-05

Differential equations, money
The increase of money in your account is proportional to the amount of money that you already have in your account. You deposit $1 per hour into your account. Model this using differential equations.
My attempt:
$y^{'} = k y + a$ where a is the portion of that $1/h. But the question is, how am I supposed to find out the correct portion of that $1/h. That is,how do I find a?

Adison Rogers 2022-11-05

Does $\sum_{n = 1}^{\infty} \frac{1}{n} ((- 1)^{n} + \frac{1}{n})$ converges?

Layton Park 2022-11-05

Notation of differential equations
I have just started a course on differential equations, and unfortunetely enough for me, we immediately used notation foreign for me, for example:
$x^{2} {(\frac{d^{2} y}{d x^{2}})}^{2} = \sin (x) and y \times \frac{d^{2} y}{d x^{2}} = \sin (x)$
were used as examples of non-linear ordinary differential equations. My questions are
- Is $\frac{d y}{d x}$ equal to y′? Also, what then is $\frac{d^{2} y}{d x^{2}}$ ?
I have looked up the formal mathematical definition but it somewhat confuses me,
- Why on earth is this notation used, instead of just using ′ or ′′? It seems to me much more confusing and unnecessarily messy.

Adison Rogers 2022-11-05

Using either the Direct or Limit Comparison Tests, determine if $\sum_{n = 2}^{\infty} \frac{1}{n \sqrt{n^{2} - 1}}$ is convergent or divergent.

Rigoberto Drake 2022-11-04

Using implicit differentiation, what is $\frac{d y}{d x}$ if $x y + 4 = x$ ?
I know the answer is $\frac{1 - y}{x}$ but I don't know how to get the answer.
So, I believe it is using a product rule. However, do I also need to use the chain rule?
What I did is
$x y + 4 = x$
I got $x + y$ using the product rule so then,
$x (\frac{d y}{d x}) + y + 0 = 1$
And is 4 a constant?
I am not sure the next step why $\frac{d y}{d x}$ belongs to $x$ instead of $y$ ? Can anyone please explains this to me?

piopiopioirp 2022-11-04

Write an integral that requires three applications of integration by parts. Explain why three applications are needed.

drogaid1d8 2022-11-04

Why the following series
$\sum_{n = 1}^{\infty} \frac{\ln n}{\sqrt{n^{3} - n + 1}}$
converges?

Rihanna Bentley 2022-11-04

Find maclaurin series using the first few terms for:
$\frac{1}{x^{2}} (\frac{\sin x}{\cos x} - x)$

MISA6zh 2022-11-03

Find all values of real number p for which the series converges absolutely
$\sum_{k = 2}^{\infty} \frac{1}{k (\log k)^{p}}$

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