G Tewani Solutions for Chapter: Applications of Derivatives, Exercise 2: DPP

Acute angle between two curves $x^2+y^2=a^2\sqrt{2}$ and $x^2-y^2=a^2$ is:

The minimum distance between a point on the curve $y=e^x$ and a point on the curve $y={\log }_{e}x$ is:

Tangents are drawn from origin to the curve $y=\sin x+$ $\cos x$. Then their points of contact lie on the curve:

If $3x+2y=1$ is a tangent to $y=f\left(x\right)$ at $x=\frac{1}{2}$. Then

$\underset{x\to 0}{\lim }\frac{x(x-1)}{f\left(\frac{e^{2x}}{2}\right)-f\left(\frac{e^{-2x}}{2}\right)}$.

The distance of point $P$ on the curve $y=x^{\frac{3}{2}}$ which is nearest to the point $M(4,0)$ from the origin is

If the equation of the normal to the curve $y=f\left(x\right)$ at $x=0$ is $3x-y+3=0$ then the value of

$\underset{x\to 0}{\lim }\frac{x^2}{\left\{f\left(x^2\right)-5f\left(4x^2\right)+4f\left(7x^2\right)\right\}}$ is:

If $L_T, L_N, L_{ST}$ and $L_{SN}$ denote the lengths of a tangent, normal, sub-tangent and sub-normal, respectively, of a curve $y=f\left(x\right)$ at a point $P(2009, 2010)$ on it, then:

Which of the following pair(s) of family is/are orthogonal?