If f(x) = left| begin{array}{ccc} sin x & cos | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & 	an x \ x^3 & x^2 & x \ 2x & 1 & x \end{array} ight|$.Expanding along the first row

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Given $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & 	an x \ x^3 & x^2 & x \ 2x & 1 & x \end{array} ight|$.Expanding along the first row:$f(x) = \sin x(x^3 - x) - \cos x(x^4 - 2x^2) + 	an x(x^3 - 2x^4)$.We need to find $\lim_{x 	o 0} \frac{f(x)}{x^2}$.$\frac{f(x)}{x^2} = \frac{\sin x}{x} \cdot \frac{x^3 - x}{x} - \cos x \cdot \frac{x^4 - 2x^2}{x^2} + \frac{	an x}{x} \cdot \frac{x^3 - 2x^4}{x}$.$\frac{f(x)}{x^2} = \frac{\sin x}{x} (x^2 - 1) - \cos x (x^2 - 2) + \frac{	an x}{x} (x^2 - 2x^3)$.Taking the limit as $x 	o 0$:$= (1)(0 - 1) - (1)(0 - 2) + (1)(0 - 0)$.$= -1 + 2 + 0 = 1$.

If $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & \tan x \\ x^3 & x^2 & x \\ 2x & 1 & x \end{array} \right|$,then $\lim_{x \to 0} \frac{f(x)}{x^2}$ is equal to

Similar Questions

$f(x) = \left| \begin{array}{ccc} x^3 & x^2 & 3x^2 \\ 1 & -6 & 4 \\ p & p^2 & p^3 \end{array} \right|$,where $p$ is a constant,then $\frac{d^3f(x)}{dx^3}$ is

If $y = \left|\begin{array}{ccc}f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c\end{array}\right|$,then $\frac{dy}{dx}$ is equal to

Let $A = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & x \end{bmatrix}$ and $A^2 = A$. If $r$ is the rank of $A$, then $r + x =$

Let $f(x) = \left| \begin{array}{ccc} 2\cos^2 x & \sin(2x) & -\sin x \\ \sin(2x) & 2\sin^2 x & \cos x \\ \sin x & -\cos x & 0 \end{array} \right|$. Then,evaluate $\int_{0}^{\frac{\pi}{2}} [f(x) + f'(x)] dx$.

If $f(x) = \left| \begin{array}{ccc} 2 \cos x & 1 & 0 \\ x - \frac{\pi}{2} & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end{array} \right|$, then $f^{\prime}(\pi)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module