Re: [考古] 96中興,化學系
※ 引述《SuzanneDuck (找回原來的自己..)》之銘言:
: 請問大家
: 96中興 微積分的第一題
: lim [√(4x^2+5x+2)+2x]
: x→-∞
: 要怎麼算 @@
: 第一題就不會解 囧~~~~
: 請高手幫忙一下
: 謝謝
lim √(4x^2 + 5x + 2) + 2x
x→-∞
(√(4x^2 + 5x + 2) + 2x)(√(4x^2 + 5x + 2) - 2x)
= lim --------------------------------------------------
x→-∞ √(4x^2 + 5x + 2) - 2x
(4x^2 + 5x + 2) - (4x^2)
= lim ---------------------------
x→-∞ √(4x^2 + 5x + 2) - 2x
5x + 2
= lim ------------------------
x→-∞ √(4x^2 + 5x + 2) - 2x
(x)(5 + (2/x))
= lim ---------------------------------------
x→-∞ (|x|)(√(4 + (5/x) + (2/(x^2)))) - 2x
(x)(5 + (2/x))
= lim --------------------------------------
x→-∞ (-x)(√(4 + (5/x) + (2/(x^2)))) - 2x
(x)(5 + (2/x))
= lim --------------------------------------
x→-∞ (-x)(√(4 + (5/x) + (2/(x^2)))) - 2x
5 + (2/x)
= lim -------------------------------------
x→-∞ (-1)(√(4 + (5/x) + (2/(x^2)))) - 2
5 + 0
= -------------------------
(-1)(√(4 + 0 + 0) - 2)
5 -5
= -------- = ----
-2 - 2 4
--
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07/06 10:18, , 1F
07/06 10:18, 1F
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