Question

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

• A. 1
• B. -1
• C. 0
• D. none of these

Answer 1

The correct option is C 0

$\underset{x\to \infty }{lim}\frac{x^5}{5^x}=\underset{x\to \infty }{lim}\frac{{5x}^4}{5^x\left(\log 5\right)}$

$=\underset{x\to \infty }{lim}\frac{{20x}^3}{5^x{\left(\log 5\right)}^2}=\underset{x\to \infty }{lim}\frac{{60x}^2}{5^x{\left(\log 5\right)}^3}$

$=\underset{x\to \infty }{lim}\frac{120x}{5^x{\left(\log 5\right)}^4}=\underset{x\to \infty }{lim}\frac{120}{5^x{\left(\log 5\right)}^5}=0$