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answered Why is $O(n^{km}+n^m)=O(n^{km})$?
May
2
comment How to prove that $\frac{\ln 12}{\ln 18}$ is irrational witout using the change of base rule?
I think your exponent for the $2$ at the end should be $h$ and not $k$.
Apr
30
comment Find range of the given function : $ f(x) = \frac{e^x}{1+ [x] } $ when $ x \ge 0 $
Just to be clear, what do you mean by $[x]$? Presumably the greatest integer $\leq x$. Also, why do you think the function is increasing in $[0,\infty)$? The question doesn't ask about montonicity.
Apr
26
reviewed Looks OK Given $\mathbb{E}[X|Y] = Y$ a.s. and $\mathbb{E}[Y|X] = X$ a.s. show $X = Y$ a.s.
Apr
26
comment How can I find the radius and interval of convergence of $\sum_{n=1}^\infty {(3x-2)^n \over n} $, and for what value x would it converge to?
The ratio test is a good start! Instead of thinking numerator/denominator, think $a_n=(3x-2)^n/n$.
Apr
24
answered Understanding Maximum Principle
Apr
23
revised Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
corrected typo
Apr
21
answered Why is $\frac{d^m}{d(-x)^m}=(-1)^m \frac{d^m}{dx^m}$
Apr
19
comment Convergence of ${a_n}$ = $\sum _1^n \frac{1}{n^{1+\alpha}}$
Are you wanting a sequence $a_n$ or a series $\sum a_n$?
Apr
10
awarded  Popular Question
Mar
12
awarded  Notable Question
Mar
3
comment Double integration for Area under a curve
Are you using $\pi$ as a variable? If so, that is poor notation. If not, then you just have $r=1$.
Mar
1
revised Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
deleted 35 characters in body
Feb
26
comment Metric Spaces: Continuous, Unbounded Functions
I'm not sure this works, but one idea that might pan out: it is enough to show there exists $t_0\in(0,1]$ since for any other $t_0\in\Bbb R$ we can take $s_0:=t_0/(\lceil t_0\rceil+1)\in(0,1)$ and then $\{f(nt_0)\}\subseteq\{f(ns_0)\}$ so that the second set is necessarily unbounded. Now one may be able to show that if $\{f(nt_0)\}$ is bounded for all $t_0\in(0,1]$, then $f(x)$ is bounded for all $x$, thereby proving the contrapositive of the statement.
Feb
7
answered Odd-degree polynomials have roots (Intermediate Value Theorem)
Feb
3
awarded  Custodian
Jan
29
awarded  Popular Question
Jan
17
comment How do I evaluate $\int u^m (1-u^2)^n du$?
@M.S.E: $n$ may be very large indeed but always finite. We aren't taking any limits here, so $n$ is a fixed constant. Keep in mind this assumes $n$ is a positive integer (which seems plausible from the context, but it hasn't been stated).
Jan
15
revised Evaluating $\lim_{x\to0} \frac{(1+x)^{1/x}-e}{x}$
added 12 characters in body
Dec
31
comment Proving if an integral is positive, negative, or zero
Out of curiosity, what are you wanting to be more rigorous? The only part I can see that could be added is that the exponential term is decreasing since the derivative is negative, hence the integral in the latter interval is smaller.