Amit M Agarwal Solutions for Chapter: Applications of Derivatives, Exercise 1: Work Book Exercise 7.1

The position of a point in time $t$ is given by $x=a+bt-c{t}^2, y=at+b{t}^2$. Its acceleration at time $t$ is

Gas is being pumped into a spherical balloon at the rate of $30 {\mathrm{ft}}^3/\min$. Then, the rate at which the radius increases when it reaches the value $15 \mathrm{ft}$, is

Water is dripping out from a conical funnel of semi-vertical angle $\frac{\pi }{4}$ at the uniform rate of $2 {\mathrm{cm}}^3/\mathrm{s}$ in the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is $4 \mathrm{cm}$, find the rate of decrease of the slant height of water, is

A stick of length $a$ cm rests against a vertical wall and the horizontal floor. If the foot of the stick slides with a constant velocity of $b \frac{\mathrm{cm}}{\mathrm{s}}$, then the magnitude of the velocity of the middle point of the stick when it is equally inclined with the floor and the wall, is

The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is $2\mathrm{cm}$ is

The approximate value of ${\left(25\right)}^{\frac{1}{3}}$ is

A cube of ice melts without changing its shape at the uniform rate of $4 {\mathrm{cm}}^3/\min$. The rate of change of the surface area of the cube, in ${\mathrm{cm}}^2/\min$, when the volume of the cube is $125 {\mathrm{cm}}^3$ is

If the radius of a sphere is measured as $7 \mathrm{m}$ with an error of $0.02 \mathrm{m}$, then the approximate error in calculating its volume is