Class 12

Math

Calculus

Application of Derivatives

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

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If there is an error of $0.1%$ in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.

Show that a rectangle of maximum perimeter which can be inscribed in a circle of radius $a$ is a square of side $2 a$.

Divide $15$ into two parts such that the square of one number multiplied with the cube of the other number is maximum.

Using differentials, find the approximate value of :$415 $

A stone is dropped into a quiet lake and waves move in circles at the speed of $5cm/s$. At the instant when the radius of the circular wave is $8cm$, how fast is the enclosed area increasing?

Using differentials, find the approximate value of :$0.24 $

Find the slope of the normal to the curve $x=acos_{3}θ,y=asin_{3}θ$ at $θ=4π $.

Find an angle $x$ which increases twice as fast as its sine.