Class 11 RD Sharma Solutions – Chapter 29 Limits – Exercise 29.10 | Set 3

Evaluate the following limits:

Question 31.

Solution:

We have,

=

=

We know,. So, we have,

= e² × log e

= e²

Question 32.

Solution:

We have,

=

Let x − π/2 = h. So, we get

=

=

We know. So, we get,

= log e

= 1

Question 33.

Solution:

We have,

=

=

=

We know,and. So, we have,

= e³ log e − 1

= e³ − 1

Question 34.

Solution:

We have,

=

=

=

We know,. So, we have,

= log e − 1

= 1 − 1

= 0

Question 35.

Solution:

We have,

=

=

=

=

We know,. So, we have,

= 3 log e − 2 log e

= 3 − 2

= 1

Question 36.

Solution:

We have,

=

=

We know,. So, we have,

= log e

= 1

Question 37., 0 < a < b

Solution:

We have,

=

=

=

=

We know,. So, we have,

= b log e − a log e

= b − a

Question 38.

Solution:

We have,

=

=

We know,and. So, we have,

= log e × 1

= 1

Question 39.

Solution:

We have,

=

=

=

We know,. So, we have,

=

= e⁰

= 1

Question 40.

Solution:

We have,

=

=

=

We know,. So, we have,

= 9 × log 3

= 9 log 3

Question 41.

Solution:

We are given,

=

=

=

=

We know,. So, we have,

=

= 2 log a

Question 42.

Solution:

We have,

=

=

=

We know,and. So, we have,

=

= 2

Question 43.

Solution:

We have,

=

=

=

=

Let x− π/2 = h in first part. So, we get,

=

We know,. So, we have,

=

=

=