[考古] 政大應數89微積分二

[ilovecurl (ilovecurl)]

6.
  In an inverse square force field 向量F= (c*向量r)/|向量r|^3,
  where c is a constant and 向量r=(x*向量i)+(y*向量j)+(z*向量k),
  find the work done in moving a particle along the line from (1,1,1)
  to (3,3,3).

  老實說我不知道這題在說什麼,想考什麼,所以無從下手
  另外同年的微積分(一)

4.For A and B positive constants,define f(x)=(e^x+Ax)^(B/x)
  a.compute L1 = lim f(x) and L2 = lim f(x)
           x->0              x-> ∞

  這個小題我算出來的答案是L1 = e^(B(1+A))   ; L2 = e^B

  b.what is the largest value of A for which the equation L1=BL2 has a
    solution? What are L1 and L2 in this case?

  根據我第一題算出來的,可以得出e^(AB)=B  A=lnB/B
  令A=lnx/x,x>0     得最大值A = 1/e 而此時 B=e
  亦可得L1和L2
  以上這樣解這題不知道對不對,請高手或是有算的人指教一下


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推 pboywc:L1算錯了 應該是e^AB
推 pboywc:阿 抱歉 我看錯了 應該沒錯 早上不清醒 囧