The volume of a cube is increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?
For the curve y = 5x – 2x³, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3.
If the radius of sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.
Find the point on the curve y = x³ – 11x + 5 at which the equation of tangent is y = x – 11.
Find the equations of the normal to the curve y = 4x³ – 3x + 5 which are perpendicular to the line 9x – y + 5 = 0..
Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.
Show that the function f given by f(x) = tan⁻¹ (sin x+ cos x) is decreasing for all
The volume of a sphere is increasing at the rate of 8 cm³/sec. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.
If P(F) = 0·35 and P(E U F) = 0·85 and E and F are independent events. Find P(E).