Continuity and Differentiability

Continuity and Differentiability
Extra questions:
1) If f(x) = is continuous at x = 0, find the value of a and b
2) A function f is defined as f(x) = for x 1 = - for x = 1. Show that f(x) is differentiable at x = 1 and find its value
3) Let f(x) = if x 2 = k, if x = 2.
If f(x) is continuous for all x, then find the value of k.
4) Let f(x) be a function of x defined as f(x) = , x 1 = , x = 1.
Discuss the continuity of function at x = 1
5) Determine the values of a, b, c for which the function f(x) = , for x < 0 = c , for x = 0 = , for x > 0
6) f(x) = , x0 is continuous at x = 0
7) Find the value of a and b so that the function is continuous at 0 x
8) Let where [ ] represents the greatest integer function. If f(x) is continuous at x = 0, then prove that a = -3 and b = -
9) . The above function is continuous and differentiable , then prove that a = , b =
10) Discuss the continuity and differentiability of the function f(x) = , 1 = ,
11) Discuss the continuity and differentiability of the function
12) Determine the constants a and b, such that the function is continuous
13) Let . If f(x) be a continuous at x = , find a and b.
14) Prove that function is discontinuous at x = 0, regardless of the value of k.
15) Find the value of k, such that function ‘f’ defined by is continuous at x =
16) Find the set of all points where the function is differentiable.
17) Let f(x) be