Question

Function whose jump (non-negative difference of LHL \& RHL) of discontinuity is greater than or equal to one, is/are -

• A. $f(x)= \begin{cases}\frac{\left(e^{1 / x}+1\right)}{\left(e^{1 / x}-1\right)} ; & x<0 \\ \frac{(1-\cos x)}{x} ; & x > 0\end{cases}$
• B. $g(x)= \begin{cases}\frac{x^{1 / 3}-1}{x^{1 / 2}-1} ; & x >1 \\ \frac{\ell n x}{(x-1)} ; & \frac{1}{2}< x< 1\end{cases}$
• C. $u(x)= \begin{cases}\frac{\sin ^{-1} 2 x}{\tan ^{-1} 3 x} & ; \quad x \in\left(0, \frac{1}{2}\right] \\ \frac{|\sin x|}{x} & ; \quad x< 0\end{cases}$
• D. $v(x)= \begin{cases}\log _3(x+2) & ; x >2 \\ \log _{1 / 2}\left(x^2+5\right) ; & x< 2\end{cases}$

Answer 1

Answer: (A), (B), (C), (D)

(A) $ LHL =-1$ &$ RHL =0$
(B) $LHL =1$ & $RHL =2 / 3$
(C) $LHL =-1$ & $RHL =2 / 3$
(D) $ LHL =-2 \log _2 3$ & $RHL =2 \log _3 2$