Jee Main
Limits Continuity And Differentiability
JEE Main 2021 (Online) 31st August Morning Shift
MCQ+4 / -12021
If the function
\(f(x) = \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x < 0} \cr k & , & {x = 0} \cr {{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} - 1}}} & , & {x > 0} \cr } } \right.\) is continuous
at x = 0, then \({1 \over a} + {1 \over b} + {4 \over k}\) is equal to :
\(f(x) = \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x < 0} \cr k & , & {x = 0} \cr {{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} - 1}}} & , & {x > 0} \cr } } \right.\) is continuous
at x = 0, then \({1 \over a} + {1 \over b} + {4 \over k}\) is equal to :