Continuity and Differentiability Questions

For a real number y, let [y] denotes the greatest integest integer less than or equal to y Then, the function f(x) is

There exists a function f(x) satisfying f(0) = 1, f′(0) = - 1 f(x) > 0 for all x and

The function f(x) = is not defined at x = 0. The value which should be assigned to f at x = 0, so that it is continuous at x = 0, is...

If f(a) = 2, f′(a) = 1, g(a) = -1, g′(a) = 2, then the value of is

is equal to

If f(x) where [x] denotes the greatest integest less than or equal to x, then f(x) equals...

If f(x) = x(√x + then

The set of all points, where the function f(x) is differentiable, is

If y2 = p(x) is a polynomial of degree 3, then equals

If f(x) = x - 1, then on the interval [0, π]

The value of

The function f(x) = [x] cos [.] denotes the greatest integer function, is discontinu ous at

Let [.] denotes the greatest integer function and f(x) = [tan2x], then

Let f(x), where p is constant. Then f(x) at x = 0 is

equals

is

The function f(x) = [x]2 -[x2] (where [x] is the greatest integer less than or equal to x), is discontinuous at...

The function f(x) = (x2 -1) |x2 -3x + 2| + cos(| x |) is not differentiable at

Let f : R → R be any function. Defion g : R → R by