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 7h answered Palaisâ€“Smale compactness condition Apr22 awarded Yearling Apr17 answered Why is the gradient of the objective function in the Lagrange multiplier theorem not $= 0$? Apr16 answered Complex Fourier coefficients for $e^{|x|}$ Apr16 comment Compute $f_x(0,0)$ etc. for the following function $f(x,y))$ You must write down the basic definition of partial derivative in terms of a quotient, and then take a limit. Apr16 comment How to practically make use of Mathematics? Most people can live well without any knowledge of higher mathematics. I can estimate that the 90% of my former students with a degree in biotechnology will never see improper integrals again. I do not know the answer to your question, since I am a mathematician and I love mathematics... Apr16 answered How to practically make use of Mathematics? Apr16 answered Multiplication and division under integral sign for non-constant function: $\int f(t)dt \iff \int f(t)\frac{g(t)}{g(t)}dt$? Apr16 comment show that $f(x)=-3x+4$ is bijective Please read the definition of injectivity: a function is one-to-one if every $y$ has at most one $x$. Apr16 answered Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$ Apr16 comment Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$ Maybe you should try to compare $a_n$ to some variant of $\sum_{k=1}^n \frac{1}{k}$. Apr15 comment I can't understand how to prove this inequality Why don't you want to compute an easy integral? Apr14 comment Integration.Matrix.Determinant.Inverse.Trace. What a bad title for this question! Apr14 answered Relative Extrema of $|x^2 - 1|$ for $-4 \leq x \leq 4$. Apr14 comment Notation issue - Asymptotic behaviour: is $\sim$ too restrictive? The big-O notation is really too weak... Apr14 answered Notation issue - Asymptotic behaviour: is $\sim$ too restrictive? Apr14 revised Short differential-form free route to understanding a specific surface integral deleted 2 characters in body; edited title Apr14 comment Differential $dx$ It is a mnemonic rule to remember the change of variable theorem for integrals, i.e. how an integral changes under the composition with a diffeomorphism. Apr14 reviewed Approve How do I prove that the set of all possible points of R lie on a circle? Apr14 comment Differential $dx$ You should think of $dx$ as the linear map $h \mapsto h$, so that $(du)h = u'(x)h$.