Mathematics Hothouse

Problem 1:

A function is defined as follows:

when

is continuous at .

The value of a should be

(i) (b) (c) 2 (d) none

Problem 2:

If when is continuous at , then what is the value of

Problem 3:

Given , when

and when

and when

if f is continuous at and and , then the value of

(i) 0 (ii) 1 (iii) 2 (iv) 3

Problem 4:

If the function is continuous on its domain where

for

for

for

then the quadratic equation whose roots are 2a and 2b is:

(i) (b) (c) (d)

Problem 5:

The value of c for which the function

when

when

is continuous at is

(i) 1/2 (ii) -1/2 (iii) 2 (iv) -2

Problem 6:

If when

, when

when

is continuous at , then a and b have the values:

(i) (ii) (iii) (iv)

Problem 7:

If , when is continuous at then

(a) 1/2 (b) -1/2 (c) 2 (d) none of these

Problem 8:

If and , then

(i) 4/3 (b) 5/3 (c) 2 (d) 7/3

Problem 9:

Evaluate the following:

Regards,

Nalin Pithwa