Limits #4

Calculus Level 3

if $f(x) = \frac{1}{3}(f(x + 1) + \frac{5}{f(x + 2)})$ and $f(x) > 0$ for all real values of x then $lim_{x \to \infty} f(x) = \sqrt\frac{a}{b}$

then a + b =

2 solutions

Akshay Bhatia
Nov 10, 2014

To Megh please upload the question clearly and close all the open brackets to avoid confusion. thankyou

Krishna Sharma
Oct 26, 2014

When $x \to \infty$

f(x) = f(x+1) = f(x +2) = t(let)

Substituting in equation we will get

3t = t + $\displaystyle \frac{5}{t}$

t = $\displaystyle \boxed{\sqrt{\frac{5}{2}}}$