Determine a and b such that f (x) is continuous at x = 0.

Find the points of discontinuity of 

Determine the form of g(x) = f ( f (x)) and hence find the point of discontinuity if g, if any.

The left hand derivative of f (x) = [x] sin (πx) at x = k, k is an integer, is:

Which of the following functions is differentiable at x = 0?

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

The function f (x) = (x² – 1) |x² – 3x +2| + cos ( | x | ) is not differentiable at

The number of points in (1, 3), where is not differentiable is: