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 10h revised Prove the following property of simple functions added 14 characters in body 2d answered Proving that $f^2$ is differentiable given that f is differentiable at $(x_0,y_0)$ 2d reviewed Approve Proving that $f^2$ is differentiable given that f is differentiable at $(x_0,y_0)$ 2d answered Property of real functions when derivative approaches zero Feb 7 answered Using definition of derivative to prove that $\lim_{h \to 0} \dfrac{f(x_0+bh)-f(x_0-ch)}{(b+c)h}=f'(x_0)$ Feb 7 revised If $u \in W^{1,p}(I) \bigcap C_c(I)$ then $u \in W_{0}^{1,p}(I)$ where $W^{1,p}(I)$ is the Sobolev Space deleted 3 characters in body Feb 7 comment Show that $\lim_{z \to 0} \frac{\Re(z)}{z}$ doesn't exist. It looks fine. Anyway, it would suffice to approach $0 \in \mathbb{C}$ first along $\mathbb{R}$ and then along $i\mathbb{R}$. Feb 7 revised Is $f( x + iy) = e^{-x} e^{-iy}$ complex - differentiable? added 1 character in body Feb 7 answered Is $f( x + iy) = e^{-x} e^{-iy}$ complex - differentiable? Feb 7 answered $\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{\sin(x)\cos(y)}$ is this done correctly? Feb 7 revised $\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{\sin(x)\cos(y)}$ is this done correctly? added 11 characters in body Feb 4 revised differentiability of a function added 14 characters in body Feb 3 revised Help evaluating the integral of $\frac{1}{1+\sqrt{1-x^2}}$ over $[0,1]$ added 5 characters in body Feb 2 comment Show that $\lim_{x \to x_0} f(x)$ exist (3) Because the limit is always unique (in a Hausdorff space). Hence you must be sure that different sequences do not lead you to different limits. Jan 31 comment Prove that $(e^x-\ln y)^2+(x-y)^2\geq 2$ Why do you believe that you can solve it without calculus of several variables? Jan 15 comment If $f\in L^2$ then there is $g$ continuous with compact support s.t. $\int (f-g)^2<\varepsilon$ You need to prove that $C_c$ is dense in $L^2$. I am unsure if you can deduce this from the density in $L^1$. Jan 14 answered $(f_n)$ in $L^p(\Omega)$ satisfying $f_n(x) \to f(x)$ a.e. and $\|f_n\|_p \to \|f\|_p$, then $\|f_n - f\|_p \to 0$? Jan 12 comment What does “proportional” mean? I guess the standard use of the proportionality symbol requires $b=0$. Jan 7 answered Exponential growth as check for integrability Jan 7 revised Is $|9x-1|^3$ differentiable at $1/9$? deleted 3 characters in body