limit-continuity-8

5) Find the point of discontinuity of where .

Solution:

The function is discontinuous at the point x=1 ----- (1)

The function is discontinuous at u=-2 and u=1.

When u = -2,

Hence composite function y = g(x) is discontinuous at three points .

6) If examine the continuity of f(x) at x=1.

Solution:

To examine the continuity at x=1, we are required to derive the definition of f(x) in the intervals x<1, x>1 and at x=1, i.e. on and around x=1.

Now if 0<x<1

So f(x) is not continuous at x=1.

Dumb Question:

1)      How does varies with the value of x?

Ans: Now suppose x<1

So,

\ =0

If x =1 then 

If x>1 then

7) Show as n® (for n ³ 6)

Solution:

Let while for n ³ 6.

\ By squeeze principle for limits,

.