Limit
2011-01-20 3:07 am
y = [(x + 4)(1 + 2/x - 15/x^2)/x]^x. Find the limit of y when x tends to infinity.
回答 (2)
2011-01-20 4:51 am
2011-01-20 4:15 am
y = [(x + 4)(1 + 2/x - 15/x^2)/x]^x
y = [(x + 2 - 15/x + 4 + 8/x - 60/x^2)/x]^x
y = (1 + 2/x - 15/x^2 + 4/x + 8/x^2 - 60/x^3)^x
y = (1 + 6/x - 7/x^2 - 60/x^3)^x
Lim (x->inifinity) y = Lim (x->infinity) (1 + 6/x - 7/x^2 - 60/x^3)^x
= 1
Since (6/x) and (-7/x^2) and (-60/x^3) -> 0 as x-> infinity
y = [(x + 2 - 15/x + 4 + 8/x - 60/x^2)/x]^x
y = (1 + 2/x - 15/x^2 + 4/x + 8/x^2 - 60/x^3)^x
y = (1 + 6/x - 7/x^2 - 60/x^3)^x
Lim (x->inifinity) y = Lim (x->infinity) (1 + 6/x - 7/x^2 - 60/x^3)^x
= 1
Since (6/x) and (-7/x^2) and (-60/x^3) -> 0 as x-> infinity
參考: Hope the solution can help you^^”
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