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SIMILAR QUESTIONS

Q1 Determine the value of ‘a’ if possible, so that the function is continuous

Q2 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).

Q3

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).

Q4

Let f  be an even function and f ’(0) exists, then find f’(0).

Q5

Let f (x) = xnn 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, ab > 0

Q6  Q7

Find the set of points where x2 |x| is true thrice differentiable.

Q8

Find the number of points where f (x) = [sin x + cos x(where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.

Q9 differentiable function in [0, 2], find a and b. (where [.] denotes the greatest integer function).

Q10

Let f : → R, such that f’ (0) = 1 and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy∀ xy Ïµ R. Find f (x).