Q. 69 - Calculus

Question

Calculate each limit in Exercises 35–80. 

$\underset{x\to 0}{lim}\frac{x}{1-\cos x}$

Step-by-Step Solution

Answer

The limit is infinity

Step 1. Given information

The given expression is $\underset{x\to 0}{lim}\frac{x}{1-\cos x}$

Step 2. Calculation

The limit is calculated as below, 

$$\begin{gathered} \left[From\mathit{ }definition, \underset{\theta \to 0}{lim}\frac{1-\cos \theta }{\theta }=0\right] \\ \underset{x\to 0}{lim}\frac{x}{1-\cos x}=\frac{1}{0} \\ =\infty \end{gathered}$$