问题 解答题

求五次多项式f(x)=a5x5+a4x4+a3x3+a2x2+a1x+a0,当x=x0(x0为任意实数)时的值.

答案

f(x)=a5x5+a4x4+a3x3+a2x2+a1x+a0=((((a5x+a4)x+a3)x+a2)x+a1)x+a0.

算法步骤如下:

第一步 计算最内层a5x+a4的值,把a5x+a4的值赋给一个变量v1

第二步 计算(a5x+a4)x+a3的值,可以改写为v1x+a3,把v1x+a3的值赋给一个变量v2

第三步 计算((a5x+a4)x+a3)x+a2的值,则该式子可改写为v2x+a2,把v2x+a2的值赋给一个变量v3

第四步 计算(((a5x+a4)x+a3)x+a2)x+a1,则该式子可改写为v3x+a1,把v3x+a1的值赋给一个变量v4

第五步 计算((((a5x+a4)x+a3)x+a2)x+a1)x+a0,则该式子可改写为v4x+a0.

以上过程可简写为

v0=a5

v1=v0x+a4

v2=v1x+a3

v3=v2x+a2

v4=v3x+a1

v5=v4x+a0.

同答案

单项选择题

(三)

The Erie Canal was the first important national waterway built in the US. It crossed New York from Buffalo on Lake Erie Troy to Albany on the Hudson River. It joined the Great Lakes with the Atlantic Ocean. The canal served as a route over which industrial goods could flow into the west, and materials could pour into the east. The Erie Canal helped New York develop into the nation’s largest city.

The building of the canal was paid for entirely by the state of New York. It cost $ 7 143 789, but it soon gained its price many times over. Between 1825, when the canal was opened, and 1882, when toll charges were stopped, the state collected $121 461 891.

For a hundred years before the Erie was built, people had been talking about a canal which could join the Great Lakes and the Atlantic Ocean. The man who planned the Erie Canal and carried the plan through was De Witt Clinton. Those who were against the canal laughingly called it "Clinton’s Ditch". Clinton talked and wrote about the canal and drew up plans for it. He and Governor Morris went to Washington in 1812 to ask for help for the canal, but they were unsuccessful.

Clinton became governor of New York in 1817, and shortly afterwards, on July 4, 1817, broke ground for the canal in Rome, N. Y. The first part of the canal was completed in 1820. As the canal grew, towns along its course developed fast. The length of the canal is 363 miles.

Which of the following is true according to the passage()

A.Clinton broke ground for the canal at both ends.

B.Clinton started building the canal before he became governor.

C.All parts of the canal were completed at the same time.

D.Construction of the canal took eight years.

单项选择题