David Mitra
Reputation
54,361
96/100 score
 6h comment Derivative of $\int \limits _x^{x^2} f(t) dt$ with respect to $x$ You forgot about the Chain Rule. 1d comment Expressing surds in different forms Multiply top and bottom by $\sqrt2$. 2d comment Piecewise monotonicity of real analytic functions Sorry, misread your question. 2d comment If $a_n$ is a null sequence, does $\sum^{\infty}_{n=1}a_n$ converge? Oh, sorry, I meant the upper limit to be "$n$". 2d comment If $a_n$ is a null sequence, does $\sum^{\infty}_{n=1}a_n$ converge? Do you want all your sums to be ${1\over n}\sum_{k=1}^\infty a_k$? Nov 27 comment If the interior of a closed set is non empty then the set is the closure of its interior? $[0,1]\cup\{2\}$. Nov 26 comment Why the plot of $\sqrt{x}$ has no negative part?? No, $\sqrt{25}$ is not $\pm 5$; it's $5$, by definition. Nov 24 comment Find the $y$-coordinate of the point $B$ with $x$-coordinate $2$ on the line through points $A(-7, -10)$ and $C(10,-1)$ The slope of the line is $9/17$ (using $A$ and $C$). The slope is also $(-10-y)/(-7-2)$ (using $A$ and $B$), where $y$ is the $y$-coordinate of $B$. Equate these two expressions and solve for $y$. Nov 24 revised Proof that $\sqrt x$ is absolutely continuous. edited tags Nov 24 revised Show a function whose derivative is bounded is also bounded in an interval edited tags Nov 22 comment Uniformly convergent and Weierstrass M-test Hmm, what is its value at $x=1$? Nov 22 comment Uniformly convergent and Weierstrass M-test Is the pointwise limit function continuous on $(-1,1]$? Nov 22 comment Probability Discrete Math Well, there are twelve months... Nov 21 comment Every Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$ You might find this useful. Nov 20 revised Show that the derivative of a function is not continuous edited tags Nov 18 comment If $\sum a_n$ (positive terms) is convergent, then $a_n \leq M/n$ for some $M$, for all $n$? What if $a_{2^n}=1/2^{n/2}$, $a_n=0$ otherwise? Nov 17 revised Find number of roots of the equation $e^x(x^4 + 4x^3 + 12x^2 + 24x + 24) + 1 = 0$ edited tags Nov 17 comment Is $\mathbb{R}^{\mathbb{R}}$ or $\mathbb{R}^{\mathbb{N}}$ separable? See Willard,Theorem 16.4, page 109. Nov 15 comment Closed and bounded but not compact in $L^p(\mathbb{R}^n)$ For $n=1$, take $f_n=\chi_{[n,n+1]}$. Do something similar for other $n$. Nov 14 comment Determining variance from sum of two random correlated variables @IanHaggerty No. See this for example.