If f(x) = | cos x x 1 2 sin x x² 2x tan x x 1 |, then lim x → 0 (f'(x))/x

(D) exists and is equal to - 2.

Limit, Continuity and Differentiability: JEE Main 2018 Mathematics question

JEE Main 2018 · 15 Apr, Morning shift · Q3666

JEE Main 201815 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,

then

\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}

JEE Main 2018 · 15 Apr, Morning shift · Q3666

JEE Main 201815 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,

then

\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}