The value of `lim_(ntooo)(e^(n))/((1+(1)/(n))^(n^(2)))`is
The value of `lim_(ntooo)(e^(n))/((1+(1)/(n))^(n^(2)))`is
A. -1
B. 0
C. 1
D. `oo`
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Correct Answer - C
`L=underset(ntooo)lim(e^(n))/((1+(1)/(n))^(n^(2)))`
`=underset(ntooo)lim(e^(n))/(e^(n^(2)log_(e)(1+(1)/(n))))`
`=underset(ntooo)lime^(n-n^(2)log_(e)(1+(1)/(n)))`
Put `n=(1)/(y)`
`:.L=underset(yto0)lime^((y-log_(e)(1+y))/(y^(2)))`
`=underset(yto0)lime^((y-(y-(y^(2))/(2)+...))/(y^(2)))`
`=e^(1//2)`
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