NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 12

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Question 15:

Prove that the function defined by

Remains discontinuous at x = 0, regardless the choice of k.

Answer:

At

And

Since, for any value of

Hence, is discontinuous at regardless the choice of

Question 16:

Find the values of and such that the function defined by

Is a continuous function at .

Answer:

Question 17:

Given the function f. Find the points of discontinuity of the composite function .

Answer:

Discontinuous at

Question 18:

Find all points of discontinuity of the function , where

Answer:

Discontinuous at and ,

Question 19:

Show that the function is continuous at . Examine the differentiability of , where is defined by

Answer:

We have

Let

And

Since, is a continuous function as it is forming with addition of two continuous function and .

Also, is also a continuous function.

Hence, is a continuous function everywhere.

So, is continuous at

Question 20:

Answer:

Not differentiable at

Question 21:

Answer:

Differentiable at

Question 22:

Answer:

Not differentiable at