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.
none of these
As, y = t2 + t |t|
and x = 2t – |t|
Thus, when t ≥ 0
âŸ¹ x = 2t – t = t, y = t2 + t2 = 2t2.
∴ x = t and y = 2t2
âŸ¹ y = 2x2 ∀ x ≥ 0.
t < 0
âŸ¹ x = 2t + t = 3t and y = t2 – t2 = 0.
âŸ¹ y = 0 for all x < 0.
Hence, f (x) = which is clearly
Continuous for all x as shown graphically.
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.
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 ……………. .