Class 11 RD Sharma Solutions - Chapter 29 Limits - Exercise 29.10 | Set 2

Evaluate the following limits:

Question 16.

Solution:

We have,

=

=

=

Asand, we get,

=

= 2

Question 17.

Solution:

We have,

=

=

=

Asand, we get,

= log e × 1

= 1

Question 18.

Solution:

We have,

=

=

=

=

=

Asand, we get,

= 1 −

=

Question 19.

Solution:

We have,

=

=

=

Let h = x/a − 1. We get,

=

We know,. So, we have,

=

=

Question 20.

Solution:

We have,

=

=

=

=

=

=

We know,. So, we have,

=

=

Question 21.

Solution:

We have,

=

=

=

=

We know,. So, we have,

=

Question 22.

Solution:

We have,

=

=

=

=

We know,. So, we have,

=

Question 23.

Solution:

We have,

=

=

=

=

=

=

We know,. So, we have,

=

=

Question 24.

Solution:

We have,

=

=

=

=

As, we get,

= log 8 − log 2

=

= log 4

Question 25.

Solution:

We have,

=

=

=

Asand, we get,

= (log 2) × 2

= 2 log 2

= log 4

Question 26.

Solution:

We have,

=

=

=

=

=

=

We know,. So, we have,

=

=

Question 27.

Solution:

We have,

=

=

=

=

We know,and. So, we get,

= 1

Question 28. 

Solution:

We have,

=

=

We know,. So, we have,

=

= a⁰ × log a

= log a

Question 29.

Solution:

We have,

=

=

=

=

=

As numerator and denominator are both zero for x = 0, therefore limit cannot exist.

Question 30. 

Solution:

We have,

=

Let x = h + 5. We get,

=

=

=

We know,. So, we have,

= e⁵ × log e

= e⁵