# Tagged Questions

75 views

### Problems with the existence of limits of several variables

I started some time studying calculus of two variables, and I'm having difficulty in knowing (and prove) that a limit does not exist, how could I resolve, for example, these, whose statement asks to ...
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### $1^\infty=1$ or is indeterminate?

$$\underbrace{1\cdot1\cdot1\cdot1\cdot1\cdot1\cdot1\cdots1\cdot1}_{\infty}=1$$ because of $1^\infty$ is indeterminate? And $$\lim_{x\to\infty}1^x=\lim_{x\to\infty}1=1?$$
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### calculate the limit of this sequence $\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1..}}}}$ [duplicate]

Possible Duplicate: $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$ i am trying to calculate the limit of ...
562 views

### prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit

i am given this problem: let $a\ge0$,$b\ge0$, and the sequences $a_n$ and $b_n$ are defined in this way: $a_0:=a$, $b_0:=b$ and $a_{n+1}:= \sqrt{a_nb_n}$ and $b_{n+1}:=\frac{1}{2}(a_n+b_n)$ for all ...
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### prove with $\epsilon$-$\delta$-argument: $x\rightarrow |-2x+3|$ is continuous

i am asked to prove with $\epsilon$-$\delta$-argument that $x\rightarrow |-2x+3|$ is continuous my steps: Definition of $\epsilon-\delta$-argument: $\forall \epsilon >0 \exists \delta>0$ with ...
58 views

### check for Continuity $x \rightarrow 2x^4-2$

Given the function: $f:\Bbb{R}\rightarrow \Bbb{R},\quad x \rightarrow 2x^4-2$ i am asked to check for Continuity for all values of $x$. i am now overasked how to do this since $\Bbb{R}$ is not a ...
102 views

### Show $\lim_{n \to \infty} \min\{a_{n},b_{n}\} = \min\{a,b\}$

If $\lim_{n \to \infty} a_{n} = a$ and $\lim_{n \to \infty} b_{n} = b$, how can we show that $\lim_{n \to \infty} \min\{a_{n},b_{n}\} = \min\{a,b\}$? I say $\min\{a_{n},b_{n}\}$ has two cases: ...
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### simple convergence test $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$

i am pulling my hair out in solving this problem. i know, it is a stupid question but i am not that good at maths, and many thanks for any help $\lim_{n \to \infty} \frac{2^{n+1}+3^{n+1}}{2^n+3^n}$ ...
### solve $\lim_{n \to \infty} \frac{(-2)^n}{3^{2n}}$
i am eating myself not being able to solve this problem. i somehow feel that the sequence converges to $0$, but once i calculate, it is not coming to that result. or am i making stupid mistake on the ...
### solve $\lim_{n \to \infty}\left( \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + i\,n\right)$
I am checking this sequence for convergence but i am not sure whether i am on the right path in calculations, these steps are what i am doing now. $\infty + n$ will go to infinity, right? \lim_{n ...