JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f\left( x \right) = \left| \begin{array}{*{20}{c}}
{\cos x}&x&1\\
{2\sin x}&{{x^2}}&{2x}\\
{\tan x}&x&1
\end{array}\right|\) , then \(\mathop {\lim }\limits_{x \to 0} \frac{{f'\left( x \right)}}{x}\)
- A Exists and is equal to \(- 2\)
- B Does not exist
- C Exist and is equal to \(0\)
- D Exists and is equal to \(2\)
Answer & Solution
Correct Answer
(A) Exists and is equal to \(- 2\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = \left| {\begin{array}{*{20}{c}} {\cos x}&x&1\\ {2\sin x}&{{x^2}}&{2x}\\ {\tan x}&x&1 \end{array}} \right|\) \( = \cos \left( {{x^2} - 2{x^2}} \right) - x\left( {2\sin x - 2x\tan x} \right)\) \( + 1\left( {2x\sin x - {x^2}\tan x} \right)\)…
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