Search found 2 matches

by xaranton
Thu Jul 07, 2016 4:29 pm
Forum: Real Analysis
Topic: function and sequence
Replies: 1
Views: 1680

function and sequence

Let \(f:[{0,1}]\longrightarrow[{0,\,1}]\) a continuous function such that \(f(0)=0\) and for every \(x,y\in[{0,1}]\) holds: \[|{f(x)-f(y)}|\geq|{x-y}|\,.\] Let, also, the sequence \(\{{x_{n}}\}_{n=1}^{\infty}\), with \(x_1\in[{0,\,1}]\) and \[x_{n+1}=f({x_{n}})\,,\;n\in\mathbb{N}\,.\] Prove that: 1)...
by xaranton
Wed Nov 25, 2015 3:28 pm
Forum: Real Analysis
Topic: Limit of function
Replies: 1
Views: 1947

Limit of function

Find the limit \[\displaystyle\mathop{\lim}\limits_{x\rightarrow+\infty}{\left({\frac{x^2+5x+4}{x^2-3x+7}}\right)^{x}}\,.\]