Problem 1:

If , where is continuous at zero, then find the value of .

Problem 2:

If for and for is continuous at and , then the find the value of .

Problem 3:

If for and for .

Consider the following statements:

i) does not exist.

ii) exists but is not defined.

iii) is discontinuous at zero

iv) exists, but is not defined.

Which of the above statements are false?

(a) all four (b) (ii) and (iv) (c) (i) and (iii) (d) none

Problem 4:

If for and for

Consider the following statements:

(i) does not exist.

(ii) does not exist.

(iii) is continuous at

(iv) is discontinuous at .

Which of the above statements are true?

(a) none (b) iv (c) iii (d) ii

Problem 5:

If the function f is continuous at and is defined by

for

for

for

The quadratic equation whose roots are values of 5a and 2b is

(a) (b)

(c) (d) none

Problem 6:

The function for and

(a) has a removable discontinuity at

(b) has irremovable discontinuity at

(c) is continuous at

(d) none of the above.

Problem 7:

If is continuous in and

when

when

when

Then, values of a and b are:

(a) 3,2 (b) 1, -2 (c) -3, 2 (d) 3,-2

Problem 8:

The value of if f is continuous on where

for

for

for is

(a) 0 (b) 2 (c) (d) indeterminate

Problem 9:

Given . Let and then

(a) f(x) is continuouis in B but discontinuous in A

(b) f(x) is discontinuous in B but continuous in A

(c) f(x) is continuous in both A and B

(d) f(x) is discontinuous in both A and B

Problem 10:

The function is

(a) continuous for all real values of x

(b) discontinuous for all real values of x

(c) discontinuous at and

(d) discontinuous at and

Regards,

Nalin Pithwa