jee-main 2018 Q78

jee-main · India · 15apr Chain Rule Limit Involving Derivative Definition of Composed Functions

If $f ( x ) = \left| \begin{array} { c c c } \cos x & x & 1 \\ 2 \sin x & x ^ { 2 } & 2 x \\ \tan x & x & 1 \end{array} \right|$, then $\lim _ { x \rightarrow 0 } \frac { f ^ { \prime } ( x ) } { x }$
(1) does not exist
(2) exists and is equal to $-2$
(3) exists and is equal to 0
(4) exists and is equal to 2

If $f ( x ) = \left| \begin{array} { c c c } \cos x & x & 1 \\ 2 \sin x & x ^ { 2 } & 2 x \\ \tan x & x & 1 \end{array} \right|$, then $\lim _ { x \rightarrow 0 } \frac { f ^ { \prime } ( x ) } { x }$\\
(1) does not exist\\
(2) exists and is equal to $-2$\\
(3) exists and is equal to 0\\
(4) exists and is equal to 2

Paper Questions

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