Let f(x)= | cos x x 1 2 sin x x^3 2 x tan x x 1 | , then lim _x arrow 0 (f(x))/(x^2)=

Correct answer: (B) -2. Hint : f(x)= (x^3-2 x^2 ) cos x+tan x (2 x^2-x^3 ) lim _x arrow 0 (f(x))/(x^2) =lim _x arrow 0(x-2) cos x+tan x(2-x) =-2

Q74 / 155 · WBJEE 2024 · Mathematics

Let $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1\end{array}\right|$, then $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=$

A
2
Correct answer
B
-2
C
1
D
-1

Solution

Hint : $\begin{aligned} & f(x)=\left(x^3-2 x^2\right) \cos x+\tan x\left(2 x^2-x^3\right) \\ & \begin{aligned} \lim _{x \rightarrow 0} \frac{f(x)}{x^2} & =\lim _{x \rightarrow 0}(x-2) \cos x+\tan x(2-x) \\ & =-2 \end{aligned} \end{aligned}$

Hence, the correct answer is option: 'B'.

Let $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1\end{array}\right|$, then $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=$

Solution

More Determinants Questions