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Mhenni Benghorbal
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 Apr 7 comment How to compute this double integral Try to change to polar coordinates. Apr 7 revised Solve this system of equations using elimination for $x(t)$ and $y(t)$ edited body Apr 7 comment Solve this system of equations using elimination for $x(t)$ and $y(t)$ @Moo typos are expected! The most important thing is the idea and the techniques! Th OP has to take care of these things!! Apr 7 comment Solve this system of equations using elimination for $x(t)$ and $y(t)$ @downvoter it is corrected! Apr 7 comment Solve this system of equations using elimination for $x(t)$ and $y(t)$ @Moo Yes it should be! Thanks for the comment. Apr 7 revised Solve this system of equations using elimination for $x(t)$ and $y(t)$ Correction Apr 7 answered Solve this system of equations using elimination for $x(t)$ and $y(t)$ Apr 7 comment If $n\in N$ and $f(x)=\ln(1+x^{2n})$, then derivative $f^{(2n)}(-1)=0$. That's the only try! Apr 6 comment Prove $f$ is not differentiable at $(0,0)$ Have you checked your notes about the differentiability of a function of two variables? Apr 6 comment Linear transformation of a subspace The image of $A$ is $4x+7y+9z=0$. Apr 6 answered variation of parameters leads to improper integral Apr 5 comment Asymptotic behaviour of the integral Make the change of variables $u=zx$ and you will be able to evaluate the integral in terms of gamma function and things will be clear. Apr 5 comment Derivative of definite integrals with interval variables inside the integral i.e.: $\frac{d}{dx} \int_a^x{(x-t)^n f^{(n+1)}(t)}dt$ You should have the answer $$\Gamma(n+1)(f'(x) + p_{n-1} ( x-a).$$ where $p_{n-1}$ is a polynomial of degree $n-1$. Apr 4 comment Definite Integral $\int_0^1 \left \{\frac{(-1)^{\lfloor 1/x \rfloor}}{x} \right\}\, dx$ You can use the techniques I gave here. Apr 2 comment Evaluate the integral using the theory of residues: $\int_0^{2\pi} \frac{(\cos \theta)^2 d \theta}{3-\sin \theta}$ Put $z=e^{i\theta}$ and consider the integral $\int_{|z|=1} f(z) dz$. Apr 1 comment Improper integral. This question has been asked several times on this website! One technique is to make a change of variables $u=\ sin x$ and then you can relate the new integral to beta function! Mar 30 comment Show that $f *g \in C(\mathbb{T})$ for $f \in L^p(\mathbb{T})$ and $g \in L^q(\mathbb{T})$ by minkowski integral inequality Writing is not clear! Mar 30 comment Uniform convergence on a closed interval - power series The series converges uniformly on any compact set within its radius of convergence. Mar 29 comment Solve for $x$ using the lambert W function $\frac{\ln(1+bx)}{x} = a$ @Did I think you have a serious problem with my answers! I can not helped it! Mar 29 comment If $\{u, v\}$ is an orthonormal set, how is $\|u - v\| = \sqrt{2}$? It should be $u. v=0$