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 2a.
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 5 cm/s. At the instant when the radius of the circular wave is 8 cm, 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=acos3θ,y=asin3θ at θ=4π.
Find an angle x which increases twice as fast as its sine.