How to evaluate <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXA

Leonel Contreras

Leonel Contreras

Answered question

2022-06-09

How to evaluate lim x 0 1 + x n 1 x , n Z

Answer & Explanation

britspears523jp

britspears523jp

Beginner2022-06-10Added 28 answers

Recall the definition of the derivative:
f ( x ) = lim h 0 f ( x + h ) f ( x ) h .
Using this, your limit is
d d x 1 + x n | x = 0 .
We have
d ( 1 + x ) 1 / n d x = 1 n ( 1 + x ) 1 / n 1 ,
so the derivative at 0 is 1 / n

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