The left hand derivative of f (x) = [x] sin (πx) at x = k, k is an integer, is:
(–1)k (k – 1)π
If x is just less than k, [x] = k – 1
Now, LHD at x = k,
Let y = f (x) be defined parametrically as y = t2 + t |t|, x = 2t – |t|, t Ïµ R Then at x = 0, find f (x) and discuss continuity.
for what value of k, f (x) is continuous at x = 0?
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.
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