[考古] 交大科管

[dododino (喔耶～)]

1. suppose f is continuous and symmetric to y-axis,f(0)=2,f(1)=1,

  f'(x)<0 (這個<我改的 題目本來是> 感覺出錯了)on (0,1),

        1
  and ∫ f(x)dx=1
       -1

(a) evaluate     1
               ∫ xf'(x)dx
                -1

(b) find     1
           ∫ f^-1 (y)dy
             0



2.  Let f be a diffrentiable function of x and y. Suppose the directional

  derivatives of f at a point A(1,3) in the direction <cosπ/4 , sin π/4 >

  and <cosπ/3 , sin π/3 > are, respectively, √2 and 2. Then

(a) Find the directional derivative of f at A in the direction

   <cos 2π/3 , sin 2π/3 >





麻煩解答了   謝謝~

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◆ From: 118.160.75.117
推 zptdaniel:1-(a)分部積分 1-(b) 變元代換
→ dododino:嗯嗯   感謝你^^
※ 編輯: dododino        來自: 118.160.75.117       (03/13 00:03)
→ dododino:不過1-b還是不太確定  有辦法再清楚一點
→ dododino:嗎  謝謝^^