Question

The value of $\underset{x\to \infty }{\lim }\frac{3^{x+1}-5^{x+1}}{3^x-5^x}$ is

• A. $5$
• B. $\frac{1}{5}$
• C. $-5$
• D. None of these

Answer 1

Answer: (A)

$\underset{x\to \infty }{\lim }\frac{3^{x+1}-5^{x+1}}{3^x-5^x}$
$=\underset{x\to \infty }{\lim }\frac{3\cdot 3^x-5\cdot 5^x}{3^x-5^x}$
$=\underset{x\to \infty }{\lim }\frac{3\cdot {\left(\frac{3}{5}\right)}^x-5}{{\left(\frac{3}{5}\right)}^x-1}=\frac{-5}{-1}$
$=5$
$(\because \underset{n\to \infty }{\lim }{a}^n=0$, if $-1<a<1)$