Tamil Nadu Board Solutions for Chapter: Applications of Differential Calculus, Exercise 2: Exercise 2

Find the slope of the tangent to the curves at the respective given points, $y=x^4+2x^2-x$ at $x=1$.

Find the tangent and normal to the following curves at the given points on the curve $y=x\sin x$ at $\left(\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$.

Find the tangent and normal to the following curves at the given points on the curves $x=\cos t, y=2{\sin }^{2}t$ at $t=\frac{\mathrm{\pi }}{3}$.

Find the equations of the tangents to the curve $y=1+x^3$ for which the tangent is orthogonal with the line $x+12y=12$.

Find the equations of the tangents to the curve $y=\frac{x+1}{x-1}$ which are parallel to the line $x+2y=6$

Find the equation of tangent and normal to the curve given by $x=7\cos t$ and $y=2\sin t, t\in R$ at any point on the curve.

Find the angle between the rectangular hyperbola $xy=2$ and the parabola $x^2+4y=0$.

Show that the two curves $x^2-y^2=r^2$ and $xy=c^2$ where $c, r$ are constants, cut orthogonally.