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

### 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,

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