[微積] 幾題考古題謝謝指點

看板Math作者jimmy780331 (lucky曉筑)時間15年前 (2011/02/09 23:13)推噓2(2推 0噓 10→)

留言12則, 4人參與討論串1/2 (看更多)

1. Prove that the function (sinx)/x is improperly integrable on [1,infinite) 稍微估計了一下在此範圍的圖形為有界的函數就一點頭緒也沒有要怎麼下手pf瑕積分 2. F(T)=(1/2T)(integral from -T to T, e^(-X^2)dx) ,T > 0 Show that F(T) is a strictly decreasing function on T 一開始我是利用 I=後面那串積分再算I^2 接著多重積分作變化但不是很容易做後來想用微積分基本定理去推就一直不知怎麼湊才對 3. Prove that f(x,y)= (x^3-xy^2)/(x^2+y^2) when (x,y)不等於(0,0) 0 when (x,y)=(0,0) is continuous, has first-order partial derivatives everywhere on R^2 but f is not differentiable at (0,0) 我先算f對x跟y的偏微然後因為兩個存在且連續去說f可一次微但我覺得這樣還不夠嚴謹且不知該如何去述說f不可在(0,0)微 4. 雙重積分exp((x+y)/(x-y))dxdy D D is the trapezoidal region with vectices (1,0),(3,0),(0,-3),(0,-1) 這題用Jacobian去算但後面給的梯形範圍沒頭緒不知怎麼變才順問題有點兒多謝謝指點感恩 <(_ _)> -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 115.82.86.211

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ilovecs34

02/09 23:53, , 1^F

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ilovecs34

02/09 23:53, , 2^F

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ilovecs34

02/09 23:54, , 3^F

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