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user284331
  • Member for 8 years, 5 months
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20 votes
Accepted

Every convergent sequence is bounded: what's wrong with this counterexample?

19 votes

Prove that $\lim_{x\rightarrow 0}\frac{f(x^2)-f(0)}{x}=0$ if $f:\mathbb{R}\rightarrow\mathbb{R}$ is differentiable at $x=0$

17 votes
Accepted

Subset of totally bounded set is totally bounded.

16 votes
Accepted

Integrating the following function

15 votes
Accepted

prove that $\lim\limits_{n\to\infty}\frac{3e^n}{n!}=0$

15 votes
Accepted

Deriving properties of logarithms from the definition $\ln(x) = \int_{1}^{x} \frac{\mathrm{d}t}{t}$

14 votes
Accepted

Proving that $\frac{f(b)-f(a)}{b-a}+ \left(\frac{g(b)-g(a)}{b-a}\right)^2\le \max_{t\in [a,b]}\{f'(t)+(g'(t))^2\}$

14 votes
Accepted

How to solve Rudin Chapter 2 problem 11?

13 votes
Accepted

Uniqueness of weak derivatives

12 votes
Accepted

Finding $\lim_{x \to \infty} x(\ln(1+x) - \ln(x))$ without l'Hopital

11 votes
Accepted

Is the Space $C^\alpha$ separable?

11 votes
Accepted

Given $f$ is absolutely integrable on $[1, \infty)$, prove that $\lim_{n \to \infty} \int_1^\infty f(x^n) dx = 0$

11 votes
Accepted

Convergence in Lp implies convergence in Lp norms finite

11 votes

Show that $e^{1-n} \leq \frac {n!}{n^n}$

10 votes
Accepted

Why iterated limits are different from simultaneous limits?

10 votes
Accepted

How to show $\min\{f_1,f_2\}$ is Lipschitz when $f_1,f_2$ are Lipschitz?

10 votes

The closure of differentiable functions are the continuous functions in the interval $[0,1]$

10 votes

Differentiability on the boundary of $[a,b]$

10 votes
Accepted

How to show $f\equiv 0$?

9 votes
Accepted

Evaluate a sum which almost looks telescoping but not quite:$\sum_{k=2}^n \frac{1}{k(k+2)}$

8 votes
Accepted

$\lim\limits_{x\to0}\sin1/x$

8 votes
Accepted

Calculate limit with L'Hopital's rule

8 votes

Determine if $\sum_{n=1}^\infty \frac{n^2}{n^3+3} $ converges or diverges

8 votes
Accepted

Prove that '$\int_E f_n\leq M$ implies $\int_E f\leq M$ ' is equivalent to Fatou's Lemma

8 votes
Accepted

Proving whether the series $\sum_{n=1}^\infty \frac{(-1)^n}{n-(-1)^n}$ converges.

8 votes
Accepted

Continuous $f$ such that $f(x)=f(x^2)$ is constant?

8 votes

Prove that $|f(x)|\le |x|+1$ for all $x\in\mathbb{R}$.

8 votes

Prove/Show that Limit is equal to 0.

8 votes
Accepted

Product of limits: If $\lim_{n\to\infty} u_nv_n=0$, does it mean that $\lim_{n\to\infty} u_n=0$ or $\lim_{n\to\infty} v_n=0$?

8 votes

If $f,g$ are continuous functions, then $fg$ is continuous?

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