Limits Continuity And Differentiability Question 92
Question: The function $ f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x} $ is not defined at $ x=\pi $ . The value of $ f(\pi ) $ so that $ f(x) $ is continuous at $ x=\pi $ is
Options:
A) $ -\frac{1}{2} $
B) $ \frac{1}{2} $
C) $ -1 $
D) $ 1 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \underset{x\to \pi }{\mathop{\lim }}\frac{1-\sin x+\cos x}{1+\sin x+\cos x} $ Using L’hospital’s rule
$ \Rightarrow \underset{x\to \pi }{\mathop{\lim }}\frac{-\cos x-sinx}{\cos x-\sin x}=\frac{-\cos \pi -\sin \pi }{\cos \pi -\sin \pi } $
$ =\frac{-(-1)-0}{-1-0}=-1 $
BETA
