Limits Continuity And Differentiability Question 72
Question: If $ \theta $ are the points of discontinuity of $ f(x)=\underset{n\to \infty }{\mathop{\lim }}{{\cos }^{2n}}x $ then the value of sin $ \theta $ is
Options:
A) 0
B) 1
C) -1
D) ½
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=\underset{n\to \infty }{\mathop{\lim }}{{({{\cos }^{2}}x)}^{n}} $
$ = \begin{matrix} 0, & 0\le {{\cos }^{2}}x<1 \\ 1, & {{\cos }^{2}}x=1 \\ \end{matrix}= \begin{matrix} 0, & x\ne n\pi ,n\in I \\ 1, & x=n\pi ,n\in I \\ \end{matrix} . . $
Hence, $ f(x) $ is discontinuous when $ x=n\pi ,n\in I $ For this values of $ \theta ,\sin \theta =0 $ .
BETA
