Find the first and second derivatives of the function f(x) = x^2 (

2022-03-11
Answered

Find the first and second derivatives of the function f(x) = x^2 (

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nick1337

Answered 2022-03-21
Author has **510** answers

Your derivative

And Second derivative

asked 2021-02-05

Use polar coordinates to find the limit. [Hint: Let $x=r\mathrm{cos}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r\mathrm{sin}$ , and note that (x, y) (0, 0) implies r 0.]
$\underset{(x,y)\to (0,0)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}$

asked 2021-09-08

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.

$P\left(x\right)=-12{x}^{2}+2136x-41000$

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

asked 2022-01-05

Differentiation of multivariable function proof

$\frac{d}{dx}{\int}_{v\left(x\right)}^{u\left(x\right)}f(t,x)dt={u}^{\prime}\left(x\right)f(u\left(x\right),x)-{v}^{\prime}\left(x\right)f(v\left(x\right),x)+{\int}_{v\left(x\right)}^{u\left(x\right)}\frac{\partial}{\partial x}f(t,x)dt$

asked 2021-06-03

Let f1,…,fr be complex polynomials in the variables x1,…,xn let V be the variety of their common zeros, and let I be the ideal of the polynomial ring

asked 2021-11-17

In a university examination, which was indeed very tough, $50\mathrm{\%}$ at jeast failed in "Statistics",$75\mathrm{\%}$ at least in Topology, $82\mathrm{\%}$ at least in "Functional Analysis" and $96\mathrm{\%}$ at least in "Applied Mathematics". How many at least failed in all the four? (Ans.$3\mathrm{\%}$ )

asked 2022-01-22

A quick question; is it possible to say in a way analogous to the single variable case that a multivariable function is "asymptotically equivalent" to a second multivariable function? For example, consider the function of $n}_{1},{n}_{2}\in \mathbb{R$ given by

$\text{Var}\left(\hat{\mu}\right)=\frac{{\sigma}^{2}({n}_{1}+2{n}_{2})}{{({n}_{1}+{n}_{2})}^{2}}.$

where$\sigma}^{2$ is a constant.

Can we say that$\text{Var}\left(\hat{\mu}\right)\approx \frac{1}{{n}_{1}+{n}_{2}}$ and then conclude that $\text{Var}\left(\hat{\mu}\right)\to 0$ as $n}_{1}\to \mathrm{\infty$ and $n}_{2}\to \mathrm{\infty$ ?

$\underset{(x,y)\to (\mathrm{\infty},\mathrm{\infty})}{lim}\frac{x+2y}{{(x+y)}^{2}}$

does not exist. Am I wrong to think of$\text{Var}\left(\hat{\mu}\right)$ as a function of two variables?

where

Can we say that

does not exist. Am I wrong to think of

asked 2021-09-09

Use the Chain Rule to find $\frac{dw}{dt}$ , where $w=\mathrm{sin}8x\mathrm{cos}2y,x=\frac{t}{2}\text{}\text{and}\text{}y={t}^{4}$

$\frac{dw}{dx}$

(Type an expression using x and y as the variables)

$\frac{dw}{dy}$

(Type an expression using x and y as the variables)

$\frac{dy}{dt}$

(Type an expression using t as the variable )

$\frac{dw}{dt}$

(Type an expression using t as the variable )

(Type an expression using x and y as the variables)

(Type an expression using x and y as the variables)

(Type an expression using t as the variable )

(Type an expression using t as the variable )