Class 11 RD Sharma Solutions – Chapter 29 Limits – Exercise 29.11

Evaluate the following limits:

Question 1. 

Solution:

We know if  such that  exists, then 

We have,

= 

= 

= e^x

Question 2. 

Solution:

We have,

= 

= 

= 

= 

= 

= 

Question 3. 

Solution:

We have,

= 

= 

= 

= 

= 

= 

= 

= 

= 

= e⁰

= 1

Question 4. 

Solution:

We have,

= 

= 

= 

= 

= 

= 

= 

= e¹⁻⁰

= e

Question 5. 

Solution:

We have,

= 

= 

= 

= 

= 

= 

= 

= e^ab−0

= e^ab

Question 6. 

Solution:

We have,

= 

= 

= 

= 

= 

Question 7. 

Solution:

We have,

= 

= 

= 

= 

= 

= 

Question 8.  

Solution:

We have,

= 

= 

Applying L’Hospital’s Rule, we get,

= 

= 

= 

= 

= 

Question 9. 

Solution:

We have,

= 

= 

= 

= 

= 

= 

= 

= 

= e^{cot a}

Question 10. 

Solution:

We have,

= 

= 

= 

= 

= e^−∞

= 1/e^∞

= 0