Q. 55 - Calculus

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given information

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

Step 2. Plug in the values

$\mathrm{If}\hspace{0.17em}\underset{x\to a-}{\lim }f\left(x\right)=\underset{x\to a+}{\lim }f\left(x\right)=L\hspace{0.17em}\mathrm{then}\hspace{0.17em}\underset{x\to a}{\lim }f\left(x\right)=L$

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

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