If y = sin px and y_n is the n^{th} derivativ | vedclass

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

Question

(B) Given $y = \sin px$. The derivatives are:$y_1 = p \cos px$$y_2 = -p^2 \sin px$$y_3 = -p^3 \cos px$$y_4 = p^4 \sin px$$y_5 = p^5 \cos px$$y_6 = -p^

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) Given $y = \sin px$. The derivatives are:$y_1 = p \cos px$$y_2 = -p^2 \sin px$$y_3 = -p^3 \cos px$$y_4 = p^4 \sin px$$y_5 = p^5 \cos px$$y_6 = -p^6 \sin px$$y_7 = -p^7 \cos px$$y_8 = p^8 \sin px$Substituting these into the determinant $D$:$D = \left| \begin{array}{ccc} \sin px & p \cos px & -p^2 \sin px \ -p^3 \cos px & p^4 \sin px & p^5 \cos px \ -p^6 \sin px & -p^7 \cos px & p^8 \sin px \end{array} ight|$Factoring out $p$ from the second column and $p^2$ from the third column:$D = p^3 \left| \begin{array}{ccc} \sin px & \cos px & -\sin px \ -p^3 \cos px & p^3 \sin px & p^3 \cos px \ -p^6 \sin px & -p^6 \cos px & p^6 \sin px \end{array} ight|$Factoring out $p^3$ from the second row and $p^6$ from the third row:$D = p^3 \cdot p^3 \cdot p^6 \left| \begin{array}{ccc} \sin px & \cos px & -\sin px \ -\cos px & \sin px & \cos px \ -\sin px & -\cos px & \sin px \end{array} ight|$Notice that the third row is the negative of the first row $(R_3 = -R_1)$.Since two rows are proportional,the value of the determinant is $0$.

If $y = \sin px$ and $y_n$ is the $n^{th}$ derivative of $y$,then $\left| \begin{array}{ccc} y & y_1 & y_2 \\ y_3 & y_4 & y_5 \\ y_6 & y_7 & y_8 \end{array} \right|$ is equal to

Similar Questions

Which one of the following statements is not correct?

If the lines $2x + y + 12 = 0$ and $kx - 3y - 10 = 0$ are conjugate with respect to the circle $x^2 + y^2 - 4x + 3y - 1 = 0$,then $k =$

The angle between the line $\frac{x + 1}{3} = \frac{y - 1}{2} = \frac{z - 2}{4}$ and the plane $2x + y - 3z + 4 = 0$ is:

Which of the following reagents can form a hydrazone with alkanone?

Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of force constant $k_{1}$ and $k_{2}$ respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body $A$ to that of body $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module