Q. The value of $\lim_{x \rightarrow 0}\frac{\sin^{2}{x + \cos{x - 1}}}{x^{2}}$ is
A) 1
B) $\frac{1}{2}$
C) $- \frac{1}{2}$
D) 0
Explanation
(b)
$\lim_{x \rightarrow 0}\frac{\sin^{2}{x + \cos{x - 1}}}{x^{2}}$
$= \lim_{x \rightarrow 0}\frac{\cos{x + \cos^{2}x}}{x^{2}}$
$= \lim_{x \rightarrow 0}{\cos x.\frac{1 - \cos x}{x^{2}}}$
$= 1.\frac{1}{2} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.