Evaluate 不12 Sin^ x dx = 「ズ「() 2 2r/2+2 n > -1 (Gamma function).

Evaluate each of the following: 1. ln(-e) 2. i^i 3. cos(i*ln(-1)) 4. cosh^-1(-1)

How many distinct values can z = i^(3i) take on?

5) A building in an apartment complex is to be built using a new modular technique. The arrangement of apartments on any floor will be chosen from one of three floor plans. The floorplan for Plan A has 4 three- bedroom units, 4 two-bedroom units, and 8 one-bedroom units. Each floor of plan B includes 3 three-bedroom units, 7 two-bedroom units, and 8 one-bedroom units. Each floor of plan C includes 5 three-bedroom units, 3 two-bedroom units, and 9 one-bedroom units. Suppose the building contains a total of x, floors of plan A, x2 floors of plan B, and x3 floors of plan C. 4 a) What does the vector x1| 4 represent? 8 b) Write a linear combination of vectors that expresses the total numbers of three-, two-, and one-bedroom apartments contained in the building. c) Is it possible to design the building with exactly 66 three-bedroom units, 74 two-bedroom units, and 136 one- bedroom units? If so, is there more than one way to do it? Explain your answer.