Q. 78 - Calculus

Question

calculate the limits of $\underset{x\to \infty }{\lim }\frac{\ln \left(x^{100}\right)}{x^8}$

Step-by-Step Solution

Answer

The limits of given function is 0

Step 1. Given information

The given function is $\underset{x\to \infty }{\lim }\frac{\ln \left(x^{100}\right)}{x^8}$

Step 2. Calculating limits

$\underset{x\to \infty }{\lim }\frac{\ln \left(x^{100}\right)}{x^8}=\underset{x\to \infty }{\lim }\frac{100\ln \left(x\right)}{x^8}$

Using L hospital rule

$$\begin{gathered} =\underset{x\to \infty }{\lim }\frac{100\times {\displaystyle \frac{1}{x}}}{8x^7} \\ =\underset{x\to \infty }{\lim }\frac{100}{8x^8} \\ =0 \end{gathered}$$

Therefore the limit is 0

Step 3. The solution

The limit of given function is 0