Mercy King
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 18h awarded Nice Answer Nov 11 comment Prove the following equation NO! there is no typo. Try to list all the numbers of the form $2k-1$ for $k=1,2,3,\ldots$, and all those of the form $2k+1$ for $k=0,1,2,\ldots$ Nov 10 revised Find and prove the limit of $X_n=$ $\frac {n^{100}}{1.01^n}$ deleted 9 characters in body Nov 10 comment Prove the following equation It is $2k-1$ if you go from $k=1$ to $\infty$, but it is $2k+1$ if you go from $k=1$ to $\infty$. Nov 10 answered Prove the following equation Nov 10 revised Prove the following equation added 18 characters in body Nov 3 answered How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$ Oct 24 revised How do you prove that $tr(B^{T} A )$ is a inner product? added 2 characters in body Oct 21 answered Find and prove the limit of $X_n=$ $\frac {n^{100}}{1.01^n}$ Oct 19 revised Express ∑sin(kx)/k as the sum of a function and the integral of another function added 120 characters in body Oct 18 answered Show that $f(x,y)$ is differentiable at $(0,0)$ Oct 18 comment Show that $f(x,y)$ is differentiable at $(0,0)$ If $f(0,0)=0$, then $df(0)\equiv0$ because $|f(h)|\le \|h\|_2^3$ for all $h \in \mathbb{R}^2$ Oct 18 comment Show that $f(x,y)$ is differentiable at $(0,0)$ The title and the problem do not match. Your title says that "show that $f$ is differentiable at $(0,0)$", however you haven't specified the value of $f(0,0)$. In fact, if $f(0,0) \ne 0$, then $f$ is not even continuous at $(0,0)$ and can not be differentiable at $(0,0)$. Oct 16 answered Find the limit of $(1+\frac{1}{n})^{n^2}/e^n$ without using derivatives Oct 16 comment What is the coordinate of a point $P$ on the line $2x-y+5=0$ such that $|PA-PB|$ is maximum where $A=(4,-2)$ and $B=(2,-4)$ Nice figure. What did you use to draw it? Oct 15 answered 1 Form Integral along the curve Oct 15 revised 1 Form Integral along the curve added 258 characters in body; edited tags Oct 12 revised Finding abs max with trig function added 38 characters in body Oct 11 answered Solve the recurrence relation $a_n=4a_{n-1}-3a_{n-2}+2^n$ with $a_1=1, a_2=11$ Oct 10 revised Prove that $\int_a^b f(x)dx=\int_{\alpha}^{\beta}f(\varphi(y))\varphi'(y)dy$ added 1 character in body; edited title