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,
=
=
=
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