Calculate this limit <munder> <mo movablelimits="true" form="prefix">lim <mrow class=

vaganzahi

vaganzahi

Answered question

2022-05-19

Calculate this limit
lim x + x ln ( x + 1 ) x ln ( x + 1 )
I need help with this one .I couldn't figure out anything that could solve it .

Answer & Explanation

redclick53

redclick53

Beginner2022-05-20Added 12 answers

Note that
x ln ( x + 1 ) x ln ( x + 1 ) = x x ln ( x + 1 ) ln ( x + 1 ) x ln ( x + 1 )
cricafh

cricafh

Beginner2022-05-21Added 3 answers

Note that x ± ln ( x + 1 ) x (the logarithm is negligible) Then
x ln ( x + 1 ) x ln ( x + 1 ) x x ln ( x + 1 ) = 1 ln ( x + 1 )
So
lim x x ln ( x + 1 ) x ln ( x + 1 ) = lim x 1 ln ( x + 1 ) = 0

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