Mathematics · 2018
JEE Main · 15 April 2018, Shift 1 · Q70
If f(x)= |cos x, x, 1; 2 sin x, x^2, 2 x; tan x, x, 1|, then lim_x → 0 (f^′(x))/x
If $\displaystyle f(x)=\left|\begin{array}{rrr}\cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1\end{array}\right|$, then
$$\lim _{x \rightarrow 0} \frac{f^{\prime}(x)}{x}
$$
Official answer
(4)
exists and is equal to -2.
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JEE Main 2018 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.