Re: [微分] 請教一題極限
※ 引述《Acrylates (金色狂風(別倒著唸))》之銘言：
: lim {√(x^2 - x + 1) - ax - b} = 0 則a,b=? (a,b是實數)
: x→∞
lim (1/x) = 0 , then [lim (1/x) ] * lim [√(x^2 - x + 1) - ax - b]
x→∞ x→∞ x→∞
= lim [√(x^2 - x + 1) - ax - b]/x = 0
x→∞
=> lim [|x|*√(1 - 1/x + 1/x^2) - ax - b ]/x = 0
x→∞
=> lim √(1 - 1/x + 1/x^2) - a - b/x = 0
x→∞
=> [ lim √(1 - 1/x + 1/x^2) - a - b/x ] + lim b/x = 0
x→∞ x→∞
=> lim √(1 - 1/x + 1/x^2) - a = 0
x→∞
=> a = 1
lim √(x^2 - x + 1) - x - b = 0
x→∞
=> lim √(x^2 - x + 1) - x = b
x→∞
=> lim [ (x^2 - x + 1) - x^2 ] / [ √(x^2 - x + 1) + x ] = b
x→∞
=> lim ( -x + 1 ) / |x|*√(1 - 1/x + 1/x^2) + x = b
x→∞
=> b = - 1/2
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→
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