(G) 
(H) 
Having seen some important indeterminate limits, notice the following expansions that can be used to evaluate limits.Evaluate
and
(i) If
then we may writeNote: We finally need to consider one last important form of limits, namely
This is an extension of the previous limit as follows:
We have seen the limits
and
.
How can we use these limits to derive the limits that we require now
Consider
. Substituting
gives
. Also, as 
Hence, our limit reduces to 
Similarly, 
Having seen some important indeterminate limits, notice the following expansions that can be used to evaluate limits.Evaluate
(a) | |
(b) | |
(c) | |
(d) | |
(e) | |
(f) | |
(g) | |
(h) |
(i) If
(ii) If
then let
. where 
Now
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