2. Find (x sin x).

(二)請為這組二位元相位偏移調變的傳送訊號找出一組合理的正交歸一基底（orthonormal basis），{f1(t), f2(t)}。（4 分）

(三)請用上一小題的合理正交歸一基底，來表示出這組二位元相位偏移調變傳送訊號的向量模式，{s0, s1}。（4 分）

(四)請 用 γ、θ、及 Q-函數來表示此通訊系統的錯誤機率Pe。這裡的 γ＝Eb/N0 是每位元的訊雜比（signal-to-noise ratio, SNR），且對 M 符元 / 訊號源（M-ary signaling）而言， 。 （8 分）

1. Find the limit.

3. Evaluate the integral

4. Evaluate the integral dydx.

5. Consider the region bounded by the graphs of y = In x, y = 0, and x = e. Find the volume of the solid formed by revolving the region about the x-axis.

6. Let y = (sin a)x, sin x ＞ 0. Find

7. Assume that constants a and b are positive. Find equations for all horizontal asymptotes for the graph of .

8. We say that the two commodities are substitute commodities if a decrease in the demand for one results in an increase in the demand for the other. Con- versely, two commodities are referred to as complementary commodities if a decrease in the demand for one results in a decrease in the demand for the other as well. Suppose that the demand equations that relate the quantities demanded x and y to the unit prices p and q of the commodities A and B respectively are  given by . Are A and B substitute, complementary or neither?