Question

Let $f\left(x\right)=1-\left|\cos x\right|$for all $xϵR$. Then

• A. $f^{{}^{\prime }}\left(\frac{\pi }{2}\right)$ does not exist
• B. $f\left(x\right)$ is continuous everywhere
• C. $f\left(x\right)$ is not differentiable everywhere
• D. $\underset{x\to {\frac{\pi }{2}}^{+}}{lim}f\left(x\right)=1$

Answer 1

Answer: (B), (D)

$f\left(x\right)$ is continuous everywhere
$\underset{x\to {\frac{\pi }{2}}^{+}}{lim}f\left(x\right)=1$

$f\left(x\right)=1-\left|\cos x\right|$
Is continuous as $\cos x$ is continuous for all $x$ gives $|\cos x|$ is also continuous
hence $1-|\cos x|$ is continuous
${lim}_{x\to \frac{\pi }{2}+}1-\cos x=1$