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