Question

The value of $\underset{y\to 2}{lim}(y-2)coseca(y-2)$ is

• A. 0
• B. 1
• C. $a$
• D. $\frac{1}{a}$

Answer 1

The correct option is D $\frac{1}{a}$

Let, $L=\underset{y\to 2}{lim}(y-2)coseca(y-2)$
Now let, $x=y-2\Rightarrow y\to 2\equiv x\to 0$
Thus $L=\underset{x\to 0}{lim}x.cosecax=\underset{x\to 0}{lim}\frac{x}{\sin ax}=\frac{1}{a}\underset{x\to 0}{lim}\frac{ax}{\sin ax}=\frac{1}{a}$