Q. 18 - Calculus

Question

Consider the limit expression

$\underset{x\to 0}{\lim }\left(x^{-3}-2x^{-1}\right)$

Calculate the limit.

Step-by-Step Solution

Answer

The limit  of the expression is $\infty$.

Step 1. Given

The given expression is 

$\underset{x\to 0}{\lim }\left(x^{-3}-2x^{-1}\right)$

Step 2. Calculation

The evaluated expression is 

$$\begin{gathered} \underset{x\to 0}{\lim }\left(x^{-3}-2x^{-1}\right) \\ =\underset{x\to 0}{\lim }\left(x^{-3}\right)-\underset{x\to 0}{\lim }\left(2x^{-1}\right) \\ =\underset{x\to 0}{\lim }\left(\frac{1}{x^3}\right)-2\underset{x\to 0}{\lim }\left(\frac{1}{x}\right) \\ =\frac{1}{0^3}-2\left(\frac{1}{0}\right) \\ =\infty -2\infty \\ =\infty \end{gathered}$$