Problem 1:

The point of discontinuity of the function:

in the closed interval are:

(a) 0 and (b) and

(c) and 0 (d)

Problem 2:

Given for and for

Consider:

(i) f(x) is discontinuous in

(ii) f(x) is discontinuous in

(iii) f(x) is continuous in

(iv) exists.

Which of the above statements are false?

(a) only 1 and 2 (b) only 2 and 4 (c) only 1 and 3 (d) none of a, b, c

Problem 3:

For the following function:

for , and

for

Consider

(i) f(x) is discontinuous in

(ii) f(x) is discontinuous in

(iii) f(x) is discontinuous in

(iv) exists

Which of the above statements are true?

(a) only 1 and 2 (b) only 2 and 4 (c) only 1 and 3 (d) none of a, b and c

Problem 4:

If the function where

for

for

is continuous at , then

(a) 6 (b) (c) 9 (d)

Problem 5:

At , the function where

, where

where

has

(a) removable discontiuity

(b) irremovable discontinuity

(c) no discontinuity

(d) none

Problem 6:

If is given to be continuous at , where

for and , then the value of k is:

(a) 2 (b) -2 (c) (d)

Problem 7:

If given function is continuous at zero and if

when and , then the value of k is :

(a) (b) (c) (d)

Problem 8:

If is continuous at , where

when and then the value of k is:

(a) (b) (c) (d)

Problem 9:

A function is defined as follows:

where and is continuous at , then find the value of k.

Problem 10:

At the point the function where

, when

when possesses

(a) removable discontinuity

(b) irremovable discontinuity

(c) no discontinuity

(d) none

Regards,

Nalin Pithwa