**Evaluate the following limits:**

**Question 31.**

**Solution:**

We have,

=

=

We know,. So, we have,

= e

^{2}× log e= e

^{2}

**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,

= e

^{3}log e − 1= e

^{3}− 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,

=

= e

^{0}= 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,

=

=

=