Evaluate the following limits:
Question 16.
Solution:
We have,
=
=
=
As
and , we get, =
= 2
Question 17.
Solution:
We have,
=
=
=
As
and , we get, = log e × 1
= 1
Question 18.
Solution:
We have,
=
=
=
=
=
As
and , we get, = 1 −
=
Question 19.
Solution:
We have,
=
=
=
Let h = x/a − 1. We get,
=
We know,
. So, we have, =
=
Question 20.
Solution:
We have,
=
=
=
=
=
=
We know,
. So, we have, =
=
Question 21.
Solution:
We have,
=
=
=
=
We know,
. So, we have, =
Question 22.
Solution:
We have,
=
=
=
=
We know,
. So, we have, =
Question 23.
Solution:
We have,
=
=
=
=
=
=
We know,
. So, we have, =
=
Question 24.
Solution:
We have,
=
=
=
=
As
, we get, = log 8 − log 2
=
= log 4
Question 25.
Solution:
We have,
=
=
=
As
and , we get, = (log 2) × 2
= 2 log 2
= log 4
Question 26.
Solution:
We have,
=
=
=
=
=
=
We know,
. So, we have, =
=
Question 27.
Solution:
We have,
=
=
=
=
We know,
and . So, we get, = 1
Question 28.
Solution:
We have,
=
=
We know,
. So, we have, =
= a0 × log a
= log a
Question 29.
Solution:
We have,
=
=
=
=
=
As numerator and denominator are both zero for x = 0, therefore limit cannot exist.
Question 30.
Solution:
We have,
=
Let x = h + 5. We get,
=
=
=
We know,
. So, we have, = e5 × log e
= e5