NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 13
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Question 23:
Show that is continuous but not differentiable at .
Answer:
We have
For continuity at ,
Hence, is continuous at .
Now,
So, is not differentiable at .
Question 24:
A function satisfies the equation for all , . Suppose that the function is differentiable at and . Prove that .
Differentiate each of the following w.r.t. (Exercises 25 to 43):
Answer:
Let satisfies the equation
Let is differentiable at and
Also,
Question 25:
Differentiate each of the following w.r.t.
Answer:
Question 26:
Differentiate each of the following w.r.t. x
Answer:
Question 27:
Answer:
Question 28:
Answer:
Question 29:
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Question 30:
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Question 31:
Answer: