Question

Evaluate:
lim [2sin(x-1)/(x-1)]
x->1​

Answer 1

Answer:

The answer is 2

Step-by-step explanation:

                  Formula to be used:

                      $\boxed{\displaystyle \lim_{x\to 0}\dfrac{\sin x}{x}=1}$

Given limit

                  $=\displaystyle \lim_{x\to 1}\dfrac{2\sin(x-1)}{x-1}$

Substitute $x-1=y\Rightarrow x=y+1$

So if $x\to 1$ then $y\to 0$  

                  $=\displaystyle \lim_{y\to 0}\dfrac{\sin y}{y}=2\times \lim_{y\to 0}\dfrac{\sin y}{y}=2(1)=2$