(1) lim ((5x^3 + 2x^2 -x +1)(x^3 -2x -1)) = 0
x→-1
(2) lim (3x^5 -x^4 +5x^2 -3x +2)^2 = 6^2 = 36
x→1
x^3 + 3x^2 - 2x + 3
(3) lim --------------------- = -3
x→0 2x^4 - 4x^2 + 5x - 1
x^4 - 3x x (x^3 - 3) 3
(4) lim ---------- = ------------ = ---
x→0 3x^3 - 4x x (3x^2 - 4) 4
x^6 - 1 (x + 1)(x^5 - x^4 + x^3 - x^2 + x -1)
(5) lim -------- = lim -------------------------------------- = -6
x→-1 x + 1 x→-1 (x + 1)
2x^2 - x -1
(6) lim -------------------- = -2/5
x→1/2 2x^3 + x^2 + 2x + 1
x^3 + x^2 + x - 3 (x-1)(x^2+2x+3) 2
(7) lim ------------------- = lim ---------------- = ---
x→1 3x^3 + 2x^2 - 4x -1 x→1 (x-1)(3x^2+5x+1) 3
2
(8) lim (3- ---)x = lim (3x-2) = -2
x→0+ x x→0+
1 1 4 (4+2x)
------ - --- -------- - -------
4+2x 4 4(4+2x) 4(4+2x)
(9) lim ---------------- = lim ---------------------
x→0 x x→0 x
-2x -1
= lim --------- = lim -------- = -1/8
x→0 4x(4+2x) x→0 2(4+2x)
25 - x^2
(10) lim -------------- = 0
x→5 (3x-6-3)^0.5
(11) 略
1 1
(12) lim (---------------- - -------------- )
x→2 2x^2 + 3x - 14 3x^2 - x - 10
1 1
= lim ( ----------- - ------------ )
x→2 (x-2)(2x+7) (x-2)(3x+5)
1 1
= lim -------------- = ---
x→2 (2x+7)(3x+5) 121
(13)～(15) 略
2x^3+x-1-f(2) (x-2)(2x^2+4x+9)
(16) (i) lim ------------- = lim ------------------ = 25
x→2 x-2 x→2 x-2
3x^2 - 2x + 1 - 3a^2 + 2a - 1 3(x+a)(x-a)-2(x-a)
(ii) lim ------------------------------ = lim --------------------
x→a x - a x→a x-a
= lim ( 3(x+a)-2 ) = 6a-2
x→a
(iii) (iv) 略
(17) 26度
(18) (i) 不存在
(ii) 不存在
(iii) lim P(t) = 200
t→6
**有錯請指正唷^^
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