Find the number of points where f (x) = [sin x + cos x] (where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.
We know [.] is not continuous at integral points.
Thus, f (x) = [sin x + cos x] will be discontinuous at those points, where
sin x + cos x is an integer, which is the case for,
Thus, the number of points at which f (x) is discontinuous is 5.
If f (x) = x + tan x and g(x) is the inverse of f (x) then g’ (x) is equal to:
If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then
Determine the value of ‘a’ if possible, so that the function is continuous
for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).
Now if it is given that there exists a positive real δ, such that f (h) = h for 0 < h < δ then find f’(x) and hence f (x).
Let f be an even function and f ’(0) exists, then find f’(0).
Let f (x) = xn, n being non-negative integer. Then find the value of n for which the equality f’(a + b) = f ’(a) + f ’ (b) is valid for all, a, b > 0
Find the set of points where x2 |x| is true thrice differentiable.
differentiable function in [0, 2], find a and b. (where [.] denotes the greatest integer function).