Limit of function with natural logarithm I need help solving this

tripiverded9

tripiverded9

Answered question

2022-01-02

Function limit using natural logarithm
Solving this issue. I tried L hospital

Answer & Explanation

soanooooo40

soanooooo40

Beginner2022-01-03Added 35 answers

Using LHospital
Tiefdruckot

Tiefdruckot

Beginner2022-01-04Added 46 answers

Fill out the form with your limit.
limxln(1+1x)1x+11x2 
and use L Hospital

Vasquez

Vasquez

Expert2022-01-09Added 669 answers

We have
x(ln(1+1x)1x)x21+x
Let x=1y. We have,
=1yln(1+y)y1y2+y
This is,
=1yln(1+y)y1y+1y+1=1y(ln(1+y)y1)+1y+1=ln(1+y)yy2+1y+1
The first limit, as y0+ can be computed by LH used twice.
12+1=12

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