Let [.] denotes the greatest integer function and f (x) = [tan2x], then:
f (x) is continuous at x = 0
Here [.] denotes the greatest integral function, thus
as – 45o < x < 45o
⇒ tan (– 45o) < tan x < tan (45o)
⇒ – 1 < tan x < 1
⇒ 0 < tan2 x < 1
Hence, f (x) = [tan2x] = 0
Hence, f (x) is zero for all values of x from (– 45o) to (45o). Thus, f (x) exists when x → 0 and also it is continuous at x = 0, f (x) is differentiable at x = 0 and has a value 0 (i.e., f (0) = 0).
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:
Let f and g be differentiable function satisfying g’ (a) = 2, g (a) = b and fog = I (identity function) Then, f’(b) is equal to:
If the function , (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then.
Let f be a real function satisfying f (x + y + z) = f (x) f (y) f (z) for all real x, y, z . If f (2) = 4 and f’ (0) = 3. Then find f (0) and f’ (2).