User Lucifer

Lucifer

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BSc undergrad with double majoring in mathematics and physics.

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limits

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epsilon-delta

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If $x_n$ is a strictly increasing sequence and $|x_n| < 1+\dfrac{1}{n}$ then $x_n$ converges to $1$ as $n$ tends to $\infty$

Aug 16, 2022

Proving the space which consists sequences of finitely many non-zero terms is incomplete with respect to $2$ -norm

Mar 11

Can you recommend me a book about the history of complex analysis?

Nov 2, 2022

How to prove $f(x) = \frac{e^{x^{2}} \sqrt {\sin x}}{\cos x}$ is continuous on $[0,1]$ using limit theorems?

Aug 6, 2022

Prove the sequence $x_n=(1+x_{n-1})/2$ converges to $1$ as $n \rightarrow \infty$ where $x_0 \in \mathbb R$

Aug 16, 2022

If $f(x) \rightarrow 0$ as $x \rightarrow a+ $ and $g(x) \geq 1$, $x \in \mathbb R $, then $\dfrac{g(x)}{f(x)} \rightarrow \infty$, $x\rightarrow a+$

Aug 17, 2022

Proving $f'(c) = 0$ using the property of differentiability and local maximum

Aug 18, 2022

if $f(a) = f(b) = 0$ and $f(c)\neq0,$ then there exist $x_1 , x_2 \in \mathbb R $ s.t $f'(x_1) > 0$ and$ f'(x_2) <0$

Aug 20, 2022

How to show the right limit at $0$ of $\dfrac{1}{x \sin (\dfrac{1}{x})}$ does not exist?

Sep 8, 2022

$2a-1< x+a < 2a+1 \implies |x+a| < 2|a|+1$

Aug 6, 2022