Find the limit of (10/(11^x))/(9/(10^x)+11/(12^x)) as x approaches infinity

 Exercise

$\lim_{x\to\infty}\frac{\frac{10}{11}^x}{\frac{9}{10}^x+\frac{11}{12}^x}$

 

The limit of the quotient of two functions is the quotient of their limits

$\frac{\lim_{x\to\infty }\left(\frac{10}{11^x}\right)}{\lim_{x\to\infty }\left(\frac{9}{10^x}+\frac{11}{12^x}\right)}$

 

Evaluate the limit $\lim_{x\to\infty }\left(\frac{10}{11^x}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{0}{\lim_{x\to\infty }\left(\frac{9}{10^x}+\frac{11}{12^x}\right)}$

 

Evaluate the limit $\lim_{x\to\infty }\left(\frac{9}{10^x}+\frac{11}{12^x}\right)$ by replacing all occurrences of $x$ by $\infty $

$\frac{0}{0}$

 

Simplify the fraction $\frac{0}{0}$ by $0$

$1$

$1$

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.