YLL討論網

1.有一數列a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#代表為根號n最接近的正整數，求a#ed_op#SUB#ed_cl#1#ed_op#/SUB#ed_cl#+a#ed_op#SUB#ed_cl#2#ed_op#/SUB#ed_cl#+a#ed_op#SUB#ed_cl#3#ed_op#/SUB#ed_cl#+....+a#ed_op#SUB#ed_cl#2003#ed_op#/SUB#ed_cl#=? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#2.x+y+z=1/x+1/y+1/z=xy+xz+yz #ed_op#BR#ed_cl#問當x+y=α，xy+2z=β有最大值(α，β)= #ed_op#BR#ed_cl##ed_op#BR#ed_cl#3.3x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-7xy+3y#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#=7 求X#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+Y#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl# 的最大值 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#4.52張撲克排，選四張，只有兩個號碼求機率 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#5.著色問題，用五種顏色去著色一個圖形(中間有一大塊連接旁邊有六塊) #ed_op#BR#ed_cl##ed_op#BR#ed_cl#6.橢圓方程式為 x#ed_op#SUP#ed_cl#2/16#ed_op#/SUP#ed_cl#+y#ed_op#SUP#ed_cl#2/9#ed_op#/SUP#ed_cl#=1，點(3,1)在橢圓內 #ed_op#BR#ed_cl#直線L、M分別過(3，1)並交橢圓於A、B，C、D #ed_op#BR#ed_cl#過A、B的切線交點為R，過C、D的切線交點為S #ed_op#BR#ed_cl#求RS的直線方程式 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#7.x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#=8y，a、b為拋物線上兩點且其切線互相垂直， #ed_op#BR#ed_cl#那兩切線分別過a、b的兩法線方程式交Y軸於s#ed_op#SUB#ed_cl#1#ed_op#/SUB#ed_cl#,s#ed_op#SUB#ed_cl#2#ed_op#/SUB#ed_cl# #ed_op#BR#ed_cl#求 1/(a,s#ed_op#SUB#ed_cl#1#ed_op#/SUB#ed_cl#)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+1/(b,s#ed_op#SUB#ed_cl#2#ed_op#/SUB#ed_cl#)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#= #ed_op#BR#ed_cl##ed_op#BR#ed_cl#8.地球最大圓周是40000公里，有一A點為東經0度，北緯45度， #ed_op#BR#ed_cl#一B點為北緯0度東經135度，求AB的最短距離 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#9.a,b,c,d為複數，|a|=|b|=|c|=|d|=1，求|a-b|#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+|a-c|#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+|a-d|#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#=? #ed_op#BR#ed_cl##ed_op#BR#ed_cl#10.1,1/2,2/2,1/3,2/3,3/3,1/4,2/4,3/4,4/4,....，m為10000以下值為1/3的個數， #ed_op#BR#ed_cl#S#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#為前n項的和，lim(n->無窮大)S#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#/n=a，求(m,a) #ed_op#BR#ed_cl##ed_op#BR#ed_cl#11.2*2階矩陣A=| 1/2 3#ed_op#SUP#ed_cl#1/2#ed_op#/SUP#ed_cl#/2| (sigma)(k=1~98 )A^k=? #ed_op#BR#ed_cl#| -3#ed_op#SUP#ed_cl#1/2#ed_op#/SUP#ed_cl#/2 1/2 | #ed_op#BR#ed_cl##ed_op#BR#ed_cl#12. #ed_op#BR#ed_cl##ed_op#BR#ed_cl#計算證明： #ed_op#BR#ed_cl##ed_op#BR#ed_cl#1.x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#-(k+3)x+(k#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+k+3)=0 有兩實根x#ed_op#SUB#ed_cl#1#ed_op#/SUB#ed_cl#,x#ed_op#SUB#ed_cl#2#ed_op#/SUB#ed_cl#，求x#ed_op#SUB#ed_cl#1#ed_op#/SUB#ed_cl##ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+x#ed_op#SUB#ed_cl#2#ed_op#/SUB#ed_cl##ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#最大值 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#2.等腰三角形一腰上的中線為K(k為定值)，請問頂角為幾度時，面積為最大 #ed_op#BR#ed_cl#3.三角形ABC中求證： #ed_op#BR#ed_cl#(1).sinA+sinB+sinC=.. #ed_op#BR#ed_cl#(2).sin(A/2)sin(B/2)sin(C/2)的最小值為1/8 #ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#