ONE MORE STEP TOWARD BETTER TOMMOROW
Saturday, 9 August 2014
chapter 6 Some Standard Limits 2
This limit is of the indeterminate form
. We can easily evaluate this limit based on the previous limit.
(Property of log)
This limit can alternatively be evaluated by using the expansion series for
(All other terms involving
This is just an obvious extension of the previous limit
We have used the following property of logarithms above:
This is again an extension of the limits seen previously. Let
. This gives
Hence, we have the limit L as
Note that for
, this limit is
is an integer, it is easy to see that the above relation holds because
can be expanded as
Now we have
. Now expand
using the Binomial theorem for a general index.For the general case, let
(all other terms tend to
August 09, 2014
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