Class 11 RD Sharma Solutions – Chapter 29 Limits – Exercise 29.10 | Set 1

Evaluate the following limits:

Question 1. 

Solution:

We have,

=

=

=

=

=

=

We know,. So, we have,

= 4 log 5

Question 2. 

Solution:

We have,

=

=

We know,. So, we have,

=

As, we get,

=

Question 3. 

Solution:

We have,

=

=

=

As, we get,

=

= (log_e a)²

Question 4. , n≠0

Solution:

We have,

=

=

As, we get,

=

=

Question 5. 

Solution:

We have,

=

=

=

=

As, we get,

= log a + log b

= log (ab)

Question 6. 

Solution:

We have,

=

=

=

=

=

=

As, we get,

= (log 3 − log 2)²

=

Question 7. 

Solution:

We have,

=

=

=

=

As, we get,

= 2(log2)²

Question 8. 

Solution:

We have,

=

=

=

=

As, we get,

= m log a − n log b

= log a^m − log bⁿ

=

Question 9. 

Solution:

We have,

=

=

=

As, we get,

= log a + log b + log c

= log (abc)

Question 10. 

Solution:

We have,

=

Let x − 2 = h. So, we get,

=

=

=

=

We know,. So, we have,

= log a

Question 11. 

Solution:

We have,

=

=

=

As, we get,

= log 5 + log 3 + log 2

= log (5×3×2)

= log 30

Question 12. 

Solution:

We have,

=

Let 1/x = h. We get,

=

=

As, we get,

= log a

Question 13. 

Solution:

We have,

=

=

=

=

=

=

Asand, we get,

=

=

=

Question 14. 

Solution:

We have,

=

=

=

As, we get,

= log a + log b − log c − log d

= log a+ log b − (log c + log d)

= log ab − log cd

=

Question 15. 

Solution:

We have,

=

=

Asand, we get,

= log e + 1

= 1 + 1

= 2