Continuity & Differentiability
Question 1: Find the second order derivatives of the function.
Answer
Let y =
Then,
Question 2: Find the second order derivatives of the function. x^{20}
Answer
Let y = x^{20}
Then,
Question 3: Find the second order derivatives of the function. x.cos x
Answer
Let y = x.cos x
Then,
Question 4: Find the second order derivatives of the function. log x
Answer
Let y = log x
Then,
Question 5: Find the second order derivatives of the function. x^{3} log x
Answer
Let y = x^{3} log x
Then,
Question 6: Find the second order derivatives of the function.
Answer
Let y =
Question 7: Find the second order derivatives of the function.
Answer
Let y =
Then,
Question 8: Find the second order derivatives of the function.
Answer
Let y =
Then,
Question 9: Find the second order derivatives of the function.
Answer
Let y =
Then,
Question 10: Find the second order derivatives of the function.
Answer
Let y =
Then,
Question 11: If
Answer
It is given that,
Then,
Hence, proved.
Question 12:
If in terms of y alone.
Answer
It is given that,
Then,
Question 13:
If
Answer
It is given that,
Then,
Hence, proved.
Question 14:
If , show that
Answer
It is given that,
Then,
Hence, proved.
Question 15:
If , show that
Answer
It is given that,
Then,
Hence, proved.
Question 16:
If , show that
Answer
The given relationship is
Taking logarithm on both the sides, we obtain
Differentiating this relationship with respect to x, we obtain
Hence, proved.
Question 17:
If , show that
Answer
The given relationship is
Then,
Hence, proved.
1. What is continuity in calculus? 
2. What is differentiability in calculus? 
3. How do you determine if a function is continuous? 
4. What is the difference between continuity and differentiability? 
5. What are the applications of continuity and differentiability in real life? 
129 videos359 docs306 tests

129 videos359 docs306 tests
