Application of ...

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm is:

The curve y = \(x^{\frac{1}{5}}\) has at (0, 0)

The equation of normal to the curve \(3x^2 – y^2\) = 8 which is parallel to the line x + 3y = 8 is

If the curve ay + \(x ^2\) = 7 and \(x ^3\) = y, cut orthogonally at (1, 1), then the value of a is:

If y = \(x^4\) – 10 and if x changes from 2 to 1.99, what is the change in y

The equation of tangent to the curve y (\(1 + x^2\)) = 2 – x, where it crosses x-axis is:

The points at which the tangents to the curve y = \(x^3\) – 12x + 18 are parallel to x-axis are:

The tangent to the curve y = \(e ^{2x}\) at the point (0, 1) meets x-axis at:

The slope of tangent to the curve x = \( t^2\) + 3t – 8, y = 2\( t^2\) – 2t – 5 at the point (2, –1) is:

The two curves \(x^3 – 3xy^2\) + 2 = 0 and \(3x^2y – y^3 \) – 2 = 0 intersect at an angle of

Let the f : R → R be defined by f (x) = 2x + cosx, then f :

Which of the following functions is decreasing on \((0, \frac{\pi}{2})\)

The function f (x) = tanx – x

If x is real, the minimum value of \(x^2\) – 8x + 17 is

The smallest value of the polynomial \(x^3 – 18x^2\) + 96x in [0, 9] is

The maximum value of sin x . cos x is