# Tagged Questions

Use this tag for questions about differential and integral calculus with more than one independent variable. Some related tags are (differential-geometry), (real-analysis), and (differential-equations).

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### Area of circle (double integral and cartesian coordinates)?

I know that the area of a circle, $x^2+y^2=a^2$, in cylindrical coordinates is $$\int\limits_{0}^{2\pi} \int\limits_{0}^{a} r \, dr \, d\theta = \pi a^2$$ But how can find the same result with a ...
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### Comprehension question about derivative in one point

Find the derivative of $f$ in $(x_{0} , y_{0})^{T}$ for: $$f(x,y)=\binom{x^4+2x^2y^2+y^4}{x^4+2x^2y^2+y^4}$$ Is it right to derivate $\partial x$ and $\partial y$ with $(x_0,y_0)^T$ ...
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### Using Line Integrals to solve Amperes Law

I have been reading the forums on how to solve the integral form of ampere's law and I have worked out that the correct way to solve it is to get rid of the dot product by realizing that |B ∙ dr| is ...
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### Integral of the level curve $ye^{2x}$

$\int_{0}^{2}\int_{0}^{4} ye^{2x}$ $dydx$ The book says the answer is $32(e^4-1)$ I had to do u-substitution when doing it, maybe that's where I went wrong. First integrating with respect to y, ...
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### Find the vector v that has norm equal to 3 and has the same direction as the vector <0,1,-1>

What I did was normalized v, which gives $v=\sqrt{0^{2}+1^{2}+-1^{2}}$ then I divided that by the norm of the vector with the same direction so that $u=\sqrt{2}/3$ and multiply that by vector v's ...
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### Is there a number that can be represented as $A^B=B^A$ after $16$ , where A and B are 2 distinct real numbers? [duplicate]

The number $16$ can be represented as $2^4=4^2$. Is there a (real) number after $16$ that can be represented as $A^B=B^A$? Where A and B are two distinct real numbers.I've checked many numbers and I'm ...
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