R S Aggarwal Solutions for Exercise 9: EXERCISE

If $x=a(\cos \theta +\theta \sin \theta ), y=a(\sin \theta -\theta \cos \theta )$, then find the value of ${\frac{dy}{dx}}_{\left(\theta =\frac{\mathrm{\pi }}{4}\right)}$.

If $x=\frac{3at}{\left(1+t^2\right)}, y=\frac{3a{t}^2}{\left(1+t^2\right)}$ and $\frac{dy}{dx}=\frac{kt}{\left(1-t^2\right)}$, then the required value of $k$ is

If $x=\frac{1-t^2}{1+t^2}, y=\frac{2t}{1+t^2}$ and $\frac{dy}{dx}=\frac{t^2-1}{kt}$, then the value of $k$ is

Find $\frac{dy}{dx}$, when $x={\cos }^{-1}\frac{1}{\sqrt{1+t^2}},y={\sin }^{-1}\frac{t}{\sqrt{1+t^2}}$

If $x=a(\theta -\sin \theta ), y=a(1-\cos \theta )$ find $\frac{dy}{dx}\text{ at }\theta =\frac{\pi }{2}$

If $x=\frac{{\sin }^{3}t}{\sqrt{\cos 2t}}, y=\frac{{\cos }^{3}t}{\sqrt{\cos 2t}}$, find $\frac{dy}{dx}$

If $x=2\cos \theta -\cos 2\theta$ and $y=2\sin \theta -\sin 2\theta$ find ${\left(\frac{d^{2}y}{d{x}^2}\right)}_{\theta =\frac{\pi }{2}}$.

If $x=a(\theta -\sin \theta ), y=a(1+\cos \theta )$ and $\frac{d^{2}y}{d{x}^2}=\frac{1}{4a}\cos e{c}^m\left(\frac{\theta }{2}\right)$, then the value of $m$ is