Q. 56 - Calculus

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given information

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

Step 2. Plug in the value

$\underset{x\to 1}{\lim }\frac{1-\cos (x-1)}{x}=\frac{1-\cos (1-1)}{1}$

$\underset{x\to 1}{\lim }\frac{1-\cos (x-1)}{x}=1-\cos \left(0\right)$

$\underset{x\to 1}{\lim }\frac{1-\cos (x-1)}{x}=1-1$

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