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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
25763 Points
one year 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
one year ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
Aditya Gupta
2080 Points
one year 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
one year 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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