所屬科目：研究所、轉學考(插大)-微積分
2. Evaluate (10%)
3. Show that (12%)
4. The cardioid r= 2(1+cosθ) is rotated about the polar axis y=o.Find the area of the surface generated. (12%)
5. Evaluate dydx (10%)
6. Convert dydx to polar coordinates and evaluate. (10%)
7. Findat the point (x,y,z)= (2,-1,1) if w=x2+y2+z2 and z3-xy+yz+y3=1 (10%)
8. Two sides of a triangle are 10cm and 15cm, and are increasing at 3cm/sec and 4cm/sec, respectively, which the included angle is π/3 and decreasing at 0.5 rad/sec. Is the third side increasing or decreasing? at what rate? (12%)
9. Suppose the utility of purchases of x,y,z units of three different kinds of product is given by , where the price per unit of the products is $2, $5, and $1, respectively. If a consumer has $90 to spend, how many units of each product should be purchased to achieve maximum utility ? (12%)
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(10%)
(12%)
dydx (10%)
dydx to polar coordinates and evaluate. (10%)
at the point (x,y,z)= (2,-1,1) if w=x2+y2+z2 and z3-xy+yz+y3=1 (10%)
, where the price per unit of the products is $2, $5, and $1, respectively. If a consumer has $90 to spend, how many units of each product should be purchased to achieve maximum utility ? (12%)