(1) }B$ø`ç (II) ‚25tæ l£Üâ.ÛŸp, ´†.Jl}

(1)

}B$ø`ç (II) ‚25tæ ( 2002/11/9) l£Üâ.ÛŸp, ´†.Jl}. (u 9 æ, 120 })

1. (u 20%, ® 10%) °-”Ì: (a) lim_x→0 sin 3x

|3x − 2| − |x + 2| £ (b) lim_n→∞(2ⁿ+ 5ⁿ)¹^/n, ¤T n ucb.

2. (u 15%) (a) qƒby = y(x) Å— y(1) = 1 £ x³− 3x²y + y⁴+ 1 = 0. ° y⁰(1)

£ y⁰⁰(1) 5M. (® 5%) (b) q x(t) = a(t − sin t), y(t) = a(1 − cos t). ° dy/dx Ê t = π/6 5M. (5%)

3. (10%) ° d dx

Z x³ x²

dt t³+ 2. 4. (10%) °

Z π/4 0

sec²θdθ

√1 + tan θ 5M.

5. (10%) ø7Õ®5, wxê§0¸[Þ A£ª. qÊÇávÈt = 0v, šr = 1.

7Êt = 1v, ®5Ü Ÿñ í7/8. (a) °ÊL<tv, ®55š. (b) ½ÊtÑÖýv, ® 5êr¾Ü.

6. (15%) q f (0) = 0, 7ú x 6= 0, ì2f(x) = x³sin 1

x. °f⁰(0) £ f⁰⁰(0)5M. J u.æÊ, ~zpÜâ.

8. (15%) q f (x) = x⁴+ 2x³/3 − 8x²− 8x + 13. ~N|w¯±5T, po5T, 1ú

|wfÇ.

9. (15%) àÇ, Åj$‘, AB = 17AD'Å'Å. zõA~ƒ(BC,. (Ä

¤4P AR ∼= 4P QR.) °x = AP U) 4P QR 5Þ Ñ|ü.

1

(1) }B$ø`ç (II) ‚25tæ l£Üâ.ÛŸp, ´†.Jl}