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

### Question 31.

Solution:

We have,

=

=

We know,. So, we have,

= e2 Ã— log e

= e2

### Question 32.

Solution:

We have,

=

Let x âˆ’ Ï€/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 âˆ’ 1

= e3 âˆ’ 1

### Question 34.

Solution:

We have,

=

=

=

We know,. So, we have,

= log e âˆ’ 1

= 1 âˆ’ 1

= 0

### Question 35.

Solution:

We have,

=

=

=

=

We know,. So, we have,

= 3 log e âˆ’ 2 log e

= 3 âˆ’ 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 âˆ’ a log e

= b âˆ’ a

### Question 38.

Solution:

We have,

=

=

We know,and. So, we have,

= log e Ã— 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 Ã— 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 xâˆ’ Ï€/2 = h in first part. So, we get,

=

We know,. So, we have,

=

=

=

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