課程名稱︰微積分乙
課程性質︰共同必修
課程教師︰張秀瑜
開課系所︰管院
考試時間︰99年11月2日
是否需發放獎勵金：是，謝謝
試題：
1.Find the limit:
sin7x
(a) lim ────
x→0 tan4x
___
2 √6-x -2
(b) lim sin (─────)
x→2 ___
√3-x -1
2.Is there a number that is exactly 5 more than its cube?
2
2x + x - 1
3.Find the horizontal and vertical asymptotes of y = ──────
2
x + 2x -3
2/3
4.Let f(x)=x . Show that f'(0) does not exist.
5.(a)Suppose f is differentiable on R and F(x)=f(cosx), find F'(x)
5 3 ___
(b)y=sec (√x+1 ) find y'
6.(a)Air is being pumped into a spherical weather balloon. At any time t, the
volume of the balloon is V(t) and its radius is r(t). What do the
dV dV
derivatives ── and ── represent?
dr dt
d
(b)If θ is measured in degree, then ── (sinθ)=?
dθ
2 2
7.Find the tangent to the ellipse x + xy + y = 3 at the point (1,1)
8.Find the critical numbers, the absolute maximum and absolute minimum of the
2
function f(θ)=2cosθ+sin θ
3 2
9.Sketch the graph of y = x + 6x + 9x
2
10.If 400 cm of material is available to make a box with a circular base and
an open top, find the largest possible volume of the box.
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