Embibe Experts Solutions for Exercise 6: Assignment

If $y=\sin 2x,$ then $\frac{d^{6}y}{d{x}^6}$ at $x=\frac{\pi }{2}$ is equal to 

Let $g\left(x\right)$ be the inverse of the function $f\left(x\right)$, and $f^{\text{'}}\left(x\right)=\frac{1}{1+x^3}$ then $g^{\text{'}}\left(x\right)$ equals

The value of $c$ according to Rolle's theorem for the function $f\left(x\right)=x^3-9x^2+26x-24$ in the interval $\left[2,4\right]$ is

The value of $c$ according to Lagrange's mean value theorem for the function $f\left(x\right)=2x^2-10x+29$ in the interval $\left[2,7\right]$ is

In $\left[0,1\right]$, Lagrange's mean value theorem is not applicable to 

If $p\left(x\right)$ be a polynomial of degree $4$, with $p\left(2\right)=-1$, $p^{\text{'}}\left(2\right)=0, p^{\text{'}\text{'}}\left(2\right)=2, p^{\text{'}\text{'}\text{'}}\left(2\right)=-12$ and $p^{\text{'}\text{'}\text{'}\text{'}}\left(2\right)=24$. Then $p^{\text{'}\text{'}}\left(1\right)$ is equal to

If $y=2{\sin }^{-1}\left(\frac{x-2}{\sqrt{6}}\right)-\sqrt{2+4x-x^2}$, then at $x=2$, find the value of $2022{\left(\frac{dy}{dx}\right)}^2$.

The number of points of discontinuity of the function $f\left(x\right)=\underset{n\to \infty }{\lim }\left[\frac{{\left(2\sin x\right)}^{2n}}{3^n-{\left(2\cos x\right)}^{2n}}\right]$, where$x\in \left[-4\pi ,4\pi \right]$, is