Find the average value of F(X/Y) =XY over the quarter circle
x^2 +y^2≦1 in the first quadrant.
2.
Evaluate F(x,y) = ∫_0^∞▒(e^(-xt)-e^(-yt))/t dt for x> 0, y:> O
3.
找出17x^2+12xy+8y^2=100上離原點最遠的座標
(這題有辦法用微積分做嗎?)
4.
Find \frac{\partial w}{\partial x} at the point (x,y,z)=(2,-1,1) if w=x^2+y^2+z^2 and z^3-xy+yz+y^3=1
這題題目有截圖可以看http://i.imgur.com/rbruCvT.jpg
5.
Two sides of a triangle are 10cm and 15cm, and are increasing at 3 cm /sec and 4 cm/ sec, respectively, which the included angle is 60° and decreasing at 0.5 rad/sec·
Is the third side increasing or decreasing? at what rate?
不好意思問題有點多，請幫我附上過程喔
謝謝
更新1:
TO 自由自在 請問一下第四題的第四行為什麼y^3不對X偏微分? 還有z^3-xy+yz+y^3=1如何變成第五行的算式?(就是Hence 上面那一行算式)
