I have the following limit. L = <munder> <mo movablelimits="true" form="prefix">lim

vittorecostao1

vittorecostao1

Answered question

2022-06-16

I have the following limit.
L = lim x 0 ( x + 4 x + 1 1 log ( x + 1 ) )

Answer & Explanation

popman14ee

popman14ee

Beginner2022-06-17Added 19 answers

Since
lim x 0 x + 4 x + 1 = 4 ,
your limit exists if and only if the limit
lim x 0 1 log ( x + 1 )
exists. But it does not exist:
since lim x 0 log ( x + 1 ) = 0 and since x > 0 log ( x + 1 ) > 0
lim x 0 + 1 log ( x + 1 ) =
since lim x 0 log ( x + 1 ) = 0 and since x < 0 log ( x + 1 ) < 0
lim x 0 1 log ( x + 1 ) =

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