## Limits and Continuity: Part 3: IITJEE maths tutorial problems

Problem 1:

Find the following limit:

Problem 2:

Let the given function be continuous in the interval . Then what must be the value of p?

, when

, when .

Problem 3:

Let the given function be continuous for , then find the most suitable values for a and b:

, for

, for

, for

Problem 4:

Find the value of the following:

Problem 5:

The function is not defined at . The value of so that f(x) becomes continuous at is (a) 1 (b) 2 (c) 0 (d) none

Problem 6:

Find the value of the following limit:

Problem 7:

Let the given function be . Find the value which should be assigned to f at so that f is continuous everywhere on the reals.

Problem 8:

Let it be given that and , x is not zero. What value of f(0) will make the function f continuous on the reals.

Problem 9:

Find the value of the following limit:

Problem 10:

If and , then the find the limiting value of as :

Problem 11:

Let it be given that . Then, the find the value of the following limit:

Problem 12:

Let it be given that when x is not zero and , when x is zero. Then, find the value of the following limit:

.

Problem 13:

Find the value of the following limit:

Problem 14:

Let it be given that when and , when is continuous at . Then, find the value of A.

Regards,

Nalin Pithwa

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