※ 引述《bitchdog (PEaCE)》之銘言：
: lim x(x+2) x^3
: x→∞ ___________ _ __________
: x + 1 x^2+1
(x)(x+2) x^3
lim ---------- - ---------
x→∞ x + 1 x^2 + 1
(x)(x+2)(x^2 + 1) - (x^3)(x+1)
= lim --------------------------------
x→∞ (x+1)(x^2 + 1)
(x)(x^3 + x + (2)(x^2) + 2) - x^4 - x^3
= lim ------------------------------------------
x→∞ x^3 + x^2 + x + 1
x^4 + x^2 + (2)(x^3) + 2x - x^4 - x^3
= lim ---------------------------------------
x→∞ x^3 + x^2 + x + 1
x^3 + x^2 + 2x
= lim -------------------
x→∞ x^3 + x^2 + x + 1
(x^3)(1 + (1/x) + (2/(x^2))
= lim ------------------------------------------
x→∞ (x^3)(1 + (1/x) + (1/(x^2)) + (1/(x^3)))
1 + (1/x) + (2/(x^2))
= lim -----------------------------------
x→∞ 1 + (1/x) + (1/(x^2)) + (1/(x^3))
1 + 0 + 0
= --------------- = 1
1 + 0 + 0 + 0
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