3.已知df(x)/dx=g(x)且h(x)=x³,則等於下列哪一個選項?
(A)g(x³)
(B)3x²g(x)
(C)g'(x)
(D)3x²g(x³)
(E)x³g(x³)。

8 Find the surface area of the portion S of the cone z2 = x2 + y2,where z ≥ 0, contained within the cylinder y2 + z2 ≤1. (A)0(B)ㅠ (C)-ㅠ (D)2ㅠ (E)-2ㅠ

1.已知3x2+2xy+y2=1， dy/dx 等於下列哪一個選項? (A) (B)(C) (D)(E) .

2.下述五個選項中,那個選項中的x取值,使得級數收斂?  (A)除了x=0之外(B)x=3(C)-3≤x≤3(D)|x|＞3 (E)對所有的x,該級數都發散。

4.就下述之極限而言,哪一個選項正確?(A)極限為1(B)極限為2(C)極限為0(D)極限為-1(E)極限不存在。

5.若對所有的實數x,F'(x)皆為連續函數,則等於下列哪一個選項? (A) 0 (B) F(0) (C) F(3) (D) F'(0) (E) F'(3)ㆍ

6. Note that z = f(x,y) where f is differentiable, x = g(t), and y = h(t). It is known that g(3)=2,g'(3)=5,h(3)=7,h'(3)=4,fx(2,7)=6,and fy(2,7)=-8. Determine the value of dz/dt at t = 3. (A)62(B) 30 (C)32 (D)-2 (E)1。

複選題7. Let g be the function given by g(x) =dt. Which of the following statements about g must be true?I. g is increasing on the interval (1,2). Ⅱ.g is increasing on the interval (2,3).III. g(3) ＞0 (A) I only (B) II only (C) II only (D) II and IIl only (E) I, I, and III。

8. If dy/dx = ysec2 c and y = 5 when x = 0, then y = (A)etanx+4(B)etanx+5(C)5etanx(D)tanx+5(E) tanx+5e。

複選題10.令l代表下列積分請問下列哪些選項是正確的? (A) I = (B)I= (C)I=∫∫Ω(x2+y2)dA,其中Ω為以(1,0)為圓心,半徑為1的圓盤 (D) I =(E) I ≤4ㅠ 

複選題11. Let A be the region bounded above by the graph of y = sin(πx) and below by the graph of y = x3 - 4x. (A)(2.1,0.8) falls into the region A. (B) The area of A can be represented bydx. (C) The area of A is equal to 4. (D)The region A is the base of a solid. For this solid, each cross section per- pendicular to the a-axis is a square.The volume of this solid is equal to dx. (E)The region A models the surface of a small pond. At all points in A tance :i from the y-axis, the depth of the water is given by h(x) = 3-x. The yolume of water in the pond is equal todx.