Calculus 2 Equations: Expert Solutions and More

Recent questions in Calculus 2
nuseldW4r 2022-12-03

Why is Taylor series expansion for $1/\left(1-x\right)$ valid only for $x\in \left(-1,1\right)$ ?

alistianyStu 2022-12-02

Prove that the equation ${4}^{x}=8x+1$ has only one solution

Julius Ho 2022-12-02

Consider the differential equation $\frac{dy}{dt}=ay-b$.Find the equilibrium solution ${y}_{e}$

e3r2a1cakCh7 2022-12-01

Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is?

Calculus 2Open question
hsupaing moe2022-11-29

A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area when the total perimeter is 16 feet.

arponatsdWT 2022-11-29

What is the product of $3$ numbers?

funnyantyLEy 2022-11-29

Evaluate the expression $C25$?

Brenda Leach 2022-11-29

Solve the given initial-value problem. The DE is homogeneous.$x{y}^{2}\frac{dy}{dx}=\frac{{y}^{3}}{{x}^{3}}$

Naomi Rowland 2022-11-27

Let $w=\frac{yz}{x}$ where and $z=r-t$. Find $\frac{\mathrm{\partial }w}{\mathrm{\partial }t}$ and $\frac{\mathrm{\partial }w}{\mathrm{\partial }r}$ by using Chain Rule.

Mollie Wise 2022-11-27

What is its worth ${15}^{\circ }$?

Harmony Oneal 2022-11-25

Suppose $\sum _{n=1}^{\mathrm{\infty }}{x}_{n}<\mathrm{\infty }$. Then prove that $\sum _{n=1}^{\mathrm{\infty }}{x}_{n}{y}_{n}$ converges.

Jamir Summers 2022-11-25

How to prove that $\underset{n\to \mathrm{\infty }}{lim}\sqrt[n]{n}=1$ ?

valahanyHcm 2022-11-25

I'm struggling somewhat to understand how to use implicit differentiation to solve the following equation:$\mathrm{cos}\mathrm{cos}\left({x}^{3}{y}^{2}\right)-x\mathrm{cot}y=-2y$I figublack that the calculation requires the chain rule to differentiate the composite function, but I'm not sure how to 'remove' the y with respect to x from inside the composite function. My calculations are:$\frac{dy}{dx}\left[\mathrm{cos}\mathrm{cos}\left({x}^{3}{y}^{2}\right)-x\mathrm{cot}y\right]=\frac{dy}{dx}\left[-2y\right]$$\frac{dy}{dx}\left[\mathrm{cos}\mathrm{cos}\left({x}^{3}{y}^{2}\right)\right]=\mathrm{sin}\mathrm{cos}\left({x}^{3}{y}^{2}\cdot {y}^{\prime }\left(x\right)\right)\cdot \mathrm{sin}\left({x}^{3}{y}^{2}\cdot {y}^{\prime }\left(x\right)\right)\cdot 6{x}^{2}y\cdot {y}^{\prime }\left(x\right)$This seems a bit long and convoluted. I'm also not sure how this will allow me to solve for ${y}^{\prime }\left(x\right)$. Carrying on...$\frac{dy}{dx}\left[x\mathrm{cot}y\right]=-{\mathrm{csc}}^{2}y\cdot {y}^{\prime }\left(x\right)$$\frac{dy}{dx}\left[-2y\right]=-2$Is my calculation correct so far? This seems to be a very complex derivative. Any comments or feedback would be appreciated.

hEorpaigh3tR 2022-11-25

What is the value of $\frac{100}{0}$? 1) 02) 13) 64) Not defined

Cherish Rivera 2022-11-24

What is the integral of log(z) over the unit circle?I tried three times, but in the end I am concluding that it equals infinity, after parametrizing, making a substitution and integrating directly (since the Residue Theorem is not applicable, because the unit circle encloses an infinite amount of non-isolated singularities.)Any ideas are welcome.Thanks,

Lorena Becker 2022-11-24

My final for my introductory analysis course is tomorrow and my teacher gave us a list of possible theorems to prove. If anyone could please show me a proof for The Intermediate Value Theorem that is short and easy to follow, so even if I still cannot understand it I can at least memorize it. Also, I have looked through numerous texts and the internet, but they all seem to confuse me. I know that itis an insult to all you math experts to memorize proofs, but I am desperate at this point. Thank you

Barrett Osborn 2022-11-23

Use the intermediate value theorem to prove that if $f:\left[1,2\right]\to R$ is a continuous function, that there is at least one number $c$ in the interval $\left(1,2\right)$ such that $f\left(c\right)=1/\left(1-c\right)+1/\left(2-c\right)$This is a question for my intro calc class that I am having a hard time understanding.

Talia Frederick 2022-11-23