# Important Questions for CBSE Class 11 Maths Chapter 13 - Limits and Derivatives

## CBSE Class 11 Maths Chapter-13 Important Questions - Free PDF Download

**1 Marks Questions**

**1. Evaluate **

**Ans.**

**2. Evaluate **

**Ans.**

=

**3. Find derivative of **

**Ans. **Let

**4. Find derivative of **

**Ans.**

**5. Evaluate **

**Ans.**

**6. What is the value of **

**Ans.**

**7. Differentiate **

**Ans.**

**8. If find **

**Ans.**

**9. Evaluate **

**Ans.**

=

=

**10. Differentiate sinwith respect to **

**Ans.**

=

**11. Evaluate **

**Ans.**

**12. Evaluate **

**Ans.**

=

=

=

**13. Find**

** **

**Ans.**

**14. Evaluate **

**Ans.**

**15. Find derivative of **

**Ans.**

**16. Find derivative of **

**Ans.**

**17. The value of **

**Ans.**

**18. Evaluate **

**Ans.**

**19. find the value of ‘a**

**Ans.**

**20. Differentiate **

**Ans.**

**4 Marks Questions**

**1. Prove that **

**Ans.** We have

=

**2. Evaluate **

**Ans. **

=

**3. Evaluate **

**Ans.**

**4. It . Show that **

**Ans. **

Hence proved

**5. Differentiate **

**Ans. **Let

**6. Let and if What are the possible value of a and b ?**

**Ans.** Given (1) =4

=

By eq.

**7. If find **

**Ans. **

**8. Differentiate **

**Ans. **

**9. Differentiate **

**Ans.** **(i)**

**(ii) **

**10. Evaluate **

**Ans. **

**11. Evaluate **

**Ans. **

**12. Evaluate **

**Ans.**

**13. Find the derivative of at **

**Ans. **

At

=

=

**14. Find the derivative of with respect to using product rule**

**Ans.** let

**15. Find the derivative of with respect to **

**Ans.** let

=

=

=

=

**16. Find **

**when **

**Ans. **

We know that

L. H. L.

R. H. L.

L. H. L. R. H. L does not exist

**17. Find the derivative of the function at Also show that **

**Ans.**

At

Hence proved

**18. Evaluate **

**Ans.**

=

**19. Find derivative of by first principle**

**Ans. **

**20. Evaluate **

**Ans.**

**21. Evaluate (if it exist)**

**Ans. **

**22. For what integers and does both**

**Ans.**

For all real number exist

For

all integral values of exist

**23. If **

**Ans. **

Differentiating w. r. t. we gill

**24. Evaluate **

**Ans.**

**25. Differentiate the function with respect to **

**Ans.**

**26. Find **

**Ans. **

**27. Find **

**Ans. **

**28. Find derivative of by first principle**

**Ans.**

**29. Find derivative of **

**Ans. **

**30. Find derivative of Ans.**

**6 Marks Questions**

**1. Differentiate tanfrom first principle.**

**Ans.**

=

=

=

=

=

**2. Differentiate From first principle.**

**Ans. **let

=

=

=

=

**3. ****Find derivative of cosec by first principle **

**Ans.**

**4. Find the derivatives of the following fuchsias:**

**Ans.** (i)

(ii)

**5. ****If for what Values of ‘a’ does exist**

**Ans.**given

a=0

L.H.L.

=

R.H.L.

exist

At exist

**6. Find the derivative of sin with respect to from first principle.**

**Ans. **let

=

=

=

=

=

**7. ****Find the derivative of from first principle**

**Ans.**

**8. Find derivative of **

**Ans.** (i)

(ii)

**9. ****Evaluate **

**Ans.**

**10. Differentiate**

**Ans.** (i)

(ii)