# Tagged Questions

Questions on the evaluation of limits.

70 views

### Finding the limit of function - irrational function

How can I find the following limit: $$\lim_{x \rightarrow -1 }\left(\frac{1+\sqrt[5]{x}}{1+\sqrt[7]{x}}\right)$$
57 views

### Why upper/lower limit always has only one value?

I am a beginner to calculus, and I have a simple question on limits. Consider the function $f(x)= 1/x$ for all real $x$. Then we know that upper limit of $x$ tends to infinity is $0$. This is because ...
38 views

### Limit in a sense of distributions

How to find $\lim_{a\rightarrow\infty} f_a$ in $D'(R)$, for $a>0$, where $f_a:R\rightarrow R$ is defined by $f_a(x)=\begin{cases}\frac{\sin{ax}}{x}&x\neq 0 \\0&x=0\end{cases}$ Thanks in ...
26 views

35 views

### limit of a sequence with roots (different index)

I have to calculate the next limit: $\lim\limits_{n \rightarrow \infty} \dfrac{2\sqrt[3]{n}-5\sqrt[5]{n^2}}{\sqrt[3]{n+1}(2-\sqrt[5]{n})}$ I've tried multiplying by the conjugate, but this give a ...
57 views

76 views

### Calculate the limit $\lim\limits_{n\to\infty}\frac{\sqrt[n]{|x-1|}+1}{(x+1)^n+1}$

How can I compute the following limit? $$\lim_{n\to\infty}\frac{\sqrt[n]{|x-1|}+1}{(x+1)^n+1}$$
115 views

### How to calculate $\lim_{n\to\infty} (2^n+3^n+\cdots+n^n)^{1/n}/n ?$

I need help in calculating the following limit. $$\lim_{n\to\infty}\frac{\sqrt[n]{2^n+3^n+\cdots +n^n}}{n}$$
237 views

### What is a simple example of a limit in the real world?

This morning, I read Wikipedia's informal definition of a limit: Informally, a function f assigns an output f(x) to every input x. The function has a limit L at an input p if f(x) is "close" to ...
65 views

### Prove that the sequence $(\frac{n^2}{n!})$ converge using epsilon delta definition.

Prove that the sequence $(\frac{n^2}{n!})$ converge using epsilon delta definition. I have never seen limit involving factorial, do anyone has any ideas? Thank you.
49 views

### Find a convergent function in metric space

Let $C[−1, 1]$ be the space of continuous functions equipped with the metric $p(f,g) = \max\{|f(x)−g(x)| \mid x \in [−1, 1]\}$. Then the sequence of functions $(f_n):[−1,1]\rightarrow \mathbb{R}$ ...
52 views

### A limit of trigonometric functions

What is the lucky way to prove it without series expansion? ...
64 views

### $x_n$ is the $n$'th positive solution to $x=\tan(x)$. Find $\lim_{n\to\infty}\left(x_n-x_{n-1}\right)$

$x_n$ is the $n$'th positive solution to $x=\tan(x)$. Find $\lim_{n\to\infty}\left(x_n-x_{n-1}\right)$.
149 views

### Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$

Alright, scratch everything below the line. Let me present one cohesive question not marred by repeated edits. The limit $\lim_{x\to a}f(x)=L$ exists iff for every $\epsilon>0$ there is a ...
48 views

### Limit of Binomial distribution

In showing us that Binomial distribution: $$B_{N,p}(n) := \binom {N}{n} p^n(1-p)^{N-n}$$ tends to Poisson's: $$P_ \lambda (n) = \dfrac {\lambda ^n}{n!}e^{-\lambda}$$where I guess lambda should be ...
68 views

### Removing the Indeterminate Form of a Limit involving Natural Logs where X approaches 1

It's pretty sad, but I've been working on this math problem for a couple of hours, now. Still scouring my Calculus textbook (Calculus Concepts and Contexts by James Stewart,) class notes, and Math ...
53 views

### proving that the following limit exist

How can I prove that the following limit exist? $$\mathop {\lim }\limits_{x,y \to 0} \frac{{x^2 + y^4 }} {{\left| x \right| + 3\left| y \right|}}$$ I tried a lot of tricks. At least assuming that ...