Question

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

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

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) $LHL=-2{\log }_{2}3$ & $RHL=2{\log }_{3}2$