# Tagged Questions

100 views

### What is $\lim_{(x,y)\to(2,2)}\frac{x^4-y^4}{x^2 - y^2}$?

I have limit: $$\lim_{(x,y)\to(2,2)}\frac{x^4-y^4}{x^2 - y^2}$$ Why is the result $8$ ?
37 views

### Prove that $\left(a_{n}\right)_{n=1}^{\infty}$ converges when $|a_{n+1}-a_{n}|<q|a_{n}-a_{n-1}|$ for $0<q<1$

I'm stuck on a homework question, and could really use some help. Here is said question: "Assume that for every $n$ the following occurs: $|a_{n+1}-a_{n}|<q|a_{n}-a_{n-1}|$ when $0<q<1$ ...
28 views

### Prove that the sequence $1+\sum_{k=1}^{n}\frac{k+1}{3^{k}+1}$ converges using Cauchy

I need some help with a homework question i'm having difficulty with. Here is the question: "Use the definition of cauchy sequence to prove that the series ...
11 views

### Weak convergence and limiting distribution

I have $X_{i} \sim Unif\left(0,1\right)$ iid random variables and have to show that $$\frac{4\sum_{i=1}^n iX_{i} - n^2}{n^{3/2}}$$ converges weakly and compute its limit. How can I do this? I would ...
26 views

### Pointwise Limits (I disagree with corrections to my homework)

I got back a homework assignment and I disagree with one of the corrections. The exercise gives us a function $f_n:[0,2\pi]\rightarrow\mathbb{R}$ for all $n\in\mathbb{N}$ and asks us to find all ...
18 views

42 views

### Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right)$ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$

I'm having trouble with this homework question: "Let there be a sequence $\left(b_{n}\right)_{n=1}^{\infty}$ such that $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$. Let there also be some ...
Evaluate lim as $x$ approaches $\infty,$ $\displaystyle[(x^3+x^2)^\frac13 - (x^3-x^2)^\frac13$.