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Question

Find the value of limx0(1+x)51x

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Solution

We will solve this by using the expansion of (1+x)5.

We saw it in binomial theorem that (a+b)n can be expanded as  (a+b)n=an+nc1 an1b+.....bn.

We don't need all the terms of (1+x)5.

(1+x)5=1+5c1x+5c2x2......x5

limx0(1+x)51x=limx0(1+5c1.x+5c2x2....)1x

=limx05x+5c2x2....xx5

=limx05+5c2x+.....x4

=5.

We don't need all the terms of (1+x)5 because they will become zero once we substitute x=0


Mathematics

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