Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: WBJEE 2019

A point is in motion along a hyperbola $y=\frac{10}{x}$ so that its abscissa $x$ increases uniformly at a rate of $1$ unit per second. Then, the rate of change of its ordinate when the point passes through $(5, 2)$

A ladder $20\mathrm{ft}$ long leans against a vertical wall. The top end slides downwards at the rate of $2\mathrm{ft}$ per second. The rate at which the lower end moves on a horizontal floor when it is $12\mathrm{ft}$ from the wall is

A particle is in motion along a curve $12y=x^3$. The rate of change of its ordinate exceeds that of abscissa in

Consider the curve $y=b{e}^{-x/a}$, where $a$ and $b$ are non-zero real numbers. Then

Tangent is drawn at any point $P(x, y)$ on a curve, which passes through $(1,1)$. The tangent cuts $x$-axis and $y$-axis at $A$ and $B$ respectively. If $AP:BP=3:1$, then

The normal to the curve $y=x^2-x+1,$ drawn at the points with the abscissa $x_1=0, x_2=-1$ and $x_3=5/2$

The equation $x\log x=3-x$

Let $f\left(x\right)=\cos \left(\frac{\pi }{x}\right),x\ne 0,$ then assuming $k$ as an integer,