For the curve y = 4x³ – 2x⁵, find all those points at which the tangent passes through the origin.
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 ?
Find the equations of the normal to the curve y = x³+ 2x + 6, which are parallel to line x + 14y + 4 = 0.
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.
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.
Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).
Find the particular solution of the differential equation given that y(0) =
If x changes from 4 to 4·01, then find the approximate change in log x.
Find the area of the parallelogram whose diagonals are represented by the vectors = and
If P(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate :
(i) P(E / F)
(ii) P(E / F)
If A and B are two independent events, then prove that the probability of occurrence of at least one of A and B is given by 1 – P(A’) · P(B’)