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