110.5.3補充
9.
設\(ABCD\)為正方形,已知正方形\(ABCD\)的面積為36,且\(\overline{AB}\)平行\(x\)軸,\(A\)、\(B\)、\(C\)三點分別在\(y=log_ax\)、\(y=2log_ax\)、\(y=3log_ax\)的圖形上,則\(a=\)?
(110彰化女中,
https://math.pro/db/thread-3514-1-1.html)
14.
請問欲使\( f(a,b)=(a+b-2)^2+(a+2b-3)^2+(a+3b-5)^2+(a+4b-8)^2 \)有最小值,此時的實數數對\((a,b)=\)?
https://math.pro/db/viewthread.php?tid=680&page=3#pid7957
[解答]
對\(a\)偏微分
\(2(a+b-2)(1)+2(a+2b-3)(1)+2(a+3b-5)(1)+2(a+4b-8)(1)=0\)
\(8a+20b-36=0\)
對\(b\)偏微分
\(2(a+b-2)(2)+2(a+2b-3)(2)+2(a+3b-5)(3)+2(a+4b-8)(4)=0\)
\(20a+60b-110=0\)
解聯立方程式得\(\displaystyle a=-\frac{1}{2}\),\(b=2\)
最小值\(\displaystyle f(-\frac{1}{2},2)=1\)
16.
設數列,\(a_n=\root 3 \of{n^2+2n+1}+\root 3 \of{n^2-1}+\root 3 \of{n^2-2n+1}\),則\(\displaystyle \frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+\ldots+\frac{1}{a_{105}}=\)?
https://math.pro/db/viewthread.php?tid=2208&page=1#pid12872