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\lim_(x->\infty )(1+(1)/(2x-2))^(x-1) without using L hospital rule

\lim_(x->\infty )(1+(1)/(2x-2))^(x-1) without using L hospital rule

Grade:11

4 Answers

Arun
25750 Points
4 years ago
Dear student
 
Please attach an image. So that it is clear every terms.
I will be happy to help you.
 
Regards
Vikas TU
14149 Points
4 years ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
Aditya Gupta
2081 Points
4 years ago
your ques is to find limit (x->infty )(1+(1)/(2x-2))^(x-1)
= limit (x->infty )(1+1/2(x-1))^(x-1)
let y= x – 1, we get
L= limit (y->infty )(1+1/2y)^y
logL= limit (y->infty )y*log(1+1/2y)
put 1/2y= z
so logL= limit (z ->0)log(1+z)/2z
or 2logL= limit (z ->0)log(1+z)/z= 1
or logL= ½ 
or L= e^(1/2)= sqrt(e)
KINDLY APPROVE :))
Manish kumar
25 Points
4 years ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
thanks 

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