# Tagged Questions

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### continuity single variable function and multivariable funtion and its parcial derivatives

Is f(x)=1/x discontinuous at point x=0 or not since its domain is x>0 and x<0? And what about f(x,y)=$\frac{xy^2}{x^2+y^2}$ continuity? And Df(x,y) exist or parcial derivatives are ...
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### Can a set in $\mathbb{R}^2$ be closed but unbounded?

Today I read "on a closed, bounded set $D$". How can a set be closed but not bounded?
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### Sufficient Conditions for Multivariate Decreasing Function

I found the following helpful theorem concerning decreasing functions but it's only valid for $\varphi:\mathbb{R}\rightarrow \mathbb{R}$, I'd like to know if it can be extended to the ...
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### Maximizing a derivative of a two-variable function in an economic application [on hold]

What is the solution to this problem: Thank You
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### Which book is appropriate for a Chemistry student that needs to learn basics about integrals?

A friend of me who is not studying mathematics now needs to deal with integrals, double integrals and triple integrals within his study of chemistry. He asked me to give him a suggestion for a basic ...
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### Find the work done by the force field in moving the particle from one point to another

Find work done by the force field F in moving the particle from $(-1, 1)$ to $(3, 2)$ This sounds good till we are given that $\textbf{F} = \dfrac{2x}{y}\textbf{ i }- \dfrac{x^2}{y^2}\textbf{ j }$ ...
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### Converting a slope field into a vector field

I have homework on slope fields where I have to graph a bunch and find the equillibrium solution, but instead of taking such a long time to graph them, I decided to use WolframAlpha. Sadly, there is ...
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### Area of the region: $\;x ≥ 0; \;−x\sqrt3 ≤ y ≤ x\sqrt3;\,\;(x−1)^2 + y^2 ≤ 1$.

Can anyone please explain how to set up the needed integral? I need to calculate the area of the region given by: $x ≥ 0,$ $-x\sqrt3 ≤ y ≤ x\sqrt3,$ $(x−1)^2 + y^2 ≤ 1$.
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### Finding a value R that maximizes the flux a vector field over half a sphere of radius R

Sorry for the bad title, couldn't think of a less convoluted way of writing it. I have to find $R\in \mathbb{R}$ so that the flux of $$F(x,y,z) = (xz - x\cos(z), -yz +y\cos(z), -4 - (x^2 + y^2))$$ ...
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### Derivative: $f_x, f_y, f_{xy}$ of function - $f(x,y)$

Let's say $f(x,y) = x^2 + 2xy +y^2$ $f'_x = 2x + 2y$ $f'_y = 2y + 2x$ $f'_{xy} = 2x + 2y$ ? Am I right about the third?
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### A limit two variables

How can I compute or prove that $\displaystyle\lim_{(x,y)\to(0,0)}\dfrac{\mathrm{e}^{xy}-1}{\sqrt{x^2+y^2}}=0$?
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### Find the volume inside

Find the volume inside the torus $\rho=\sin\phi$. First of all how can $\rho=\sin\phi$ represent a torus? I can't even visualise that. All Ideas are welcome, this looks like a 'food for thought ...
### Find $\int_0^1 \int_{3x}^3 (x^2+y^2)\sqrt{9-y^2}\hspace{1mm}dy dx$ [closed]
You can use a calculator after simplification if its not possible by hand All Ideas will be appreciated Also If you could find $$\int_0^1 \int_{3x}^3 x(x^2+y^2)\sqrt{9-y^2}\hspace{1mm}dy dx$$ ...
### Maximum and minimum of $z=\frac{1+x-y}{\sqrt{1+x^2+y^2}}$
Find the maximum and minimum of the function $$z=\frac{1+x-y}{\sqrt{1+x^2+y^2}}$$ I have calculated $\frac{\partial z}{\partial x}=\frac{1+y^2+xy-x}{(1+x^2+y^2)^{\frac{3}{2}}}$ \$\frac{\partial ...