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99年 - 99下1高二數學 - 臺東縣國立臺東高商99 下學期高二數學第一次段考(期中考)#55472
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4. Find the smallest equivalence relation on {1,2,3} that contains (1,2). (12 pts) Justify your answer.
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5. How many nonnegative integer solutions are there to the equation x1 x2 + x3 + x4 = 21 such that (12 pts) Show enough work to get full credits.
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6. Apply Dijkstra’s Algorithm to find a shortest path from a to f. Indicate what is your shortest path and the total weight of the path. You must show every step in order to get full credits. (14 pts)
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7. Use mathematical induction to prove that 3 divides n3+2n whenever n is a nonnegative integer. (15 pts) (3整除n3+2n, n為非負整數)(必須以歸納證明的方法證得)
#208753
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