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Calculate the limit. Please help me out. Ty in advance

Calculate the limit. Please help me out. Ty in advance

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Grade:12

3 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
apply log on both sides 
y =x[(x/x+1)^x – 1/e] 
log y = logx + xlog(x/x+1) – lodx/e 
log y = xlog x/x+1 + loge 
log y = x log x/x+1 + loge 
log y =log e 
y = e 
Hope this helps 
Aditya Gupta
2081 Points
4 years ago
hello madhav obviously vikas answer is wrong as he has applied logarithm rules incorrectly.
this limit is actually a difficult limit. first, you need to write y= (x/(x+1))^x as e^logy= e^[x*log(x/(x+1))]. now, you need to write log(x/(x+1)) as log(1 – 1/(x+1)) and then do its series expansion using the std expansion log(1 – z)= – (z+z^2/2+z^3/3+......). obviously in our case z= 1/(x+1). then you need to multiply and divide by e and use the result lim p tends to 0 (e^p – 1)/p= 1. the limit will then become elementary.
answer is 1/(2e).
kindly approve :=)
TEJA KRISHNA
42 Points
4 years ago
 
apply log on both sides 
y =x[(x/x+1)^x – 1/e] 
log y = logx + xlog(x/x+1) – lodx/e 
log y = xlog x/x+1 + loge 
log y = x log x/x+1 + loge 
log y =log e 
y = e 

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