[考古] 暨南 91 + 95
首先是91資工的兩題
5.
-- 2xy
| -------------- , (x,y)≠(0,0)
| 2 2
| x +y
Set f(x,y)= |
| 0 , (x,y)=(0,0)
--
<partial>f
(e) Show that -------------- is discontinuous at (0,0).
<partial>x
(註：Parital 的符號打不出來，所以用<partial>代替。)
kt
6. [Hint : if f'(t)=kf(t) , then f(t)=f(0)e ]
2 2
Determine the path of steepest descent along the surface z=x +3y
from the point (1,1,4) to the point (0,0,0).
再來是95資工的一題
x
3. Definition : If z is irrational, then by e we mean the unique number
x
which has logarithm z, i.e. ln e = z .
d x x
Prove ----- (e ) = e for all real x.
dx
最近在寫各校的考古題，這三題不太知道怎麼下筆‧‧‧‧‧‧
麻煩高手幫忙解答一下囉 謝謝 ︿︿
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