Question

limx → 1⁡ (x-1)Tan(^πx⁄2) is?

(a) 0

(b) –^1⁄π

(c) –^2⁄π

(d) ^2⁄π

This question was addressed to me in examination.

Query is from Limits and Derivatives of Several Variables in chapter Partial Differentiation of Engineering Mathematics

Answer 1

The correct choice is (c) –^2⁄π

Best explanation: \(\lim_{x\rightarrow 1}\frac{(x-1)sin(\frac{\pi x}{2})}{cos(\frac{\pi x}{2})}=\frac{0}{0}\) (Indeterminate)

By L’Hospital rule

\(\lim_{x\rightarrow 1}\frac{(x-1)cos(\frac{\pi x}{2})\frac{\pi}{2}+sin(\frac{\pi x}{2})}{\frac{\pi}{2}sin(\frac{x\pi}{2})}=-\frac{2}{\pi}\)