1.f(x,y)=ln(x^2+y^2)的定義域為何?
2.承上題,其值域為何?
3. g(x,y)=sin(1/xy)於何處不連續
4若f(x,y)=tan(x+y+z),則f[x], f[y]及f[z]為何?
5. f(x,y)=ln(x)+ln(y)在p[o](1,1)的線性化方程式L(x,y)為何?
6承上題,在求算上界時,令R:|x-2|≤0.1 , |y-2|≤0.1,可得其M為何?
7. 再應用|E(x,y)|≤1/2M(|x-x[0]|+|y-x[0]|)^2,可求得其上界為何?
8f(x,y,z)=√(x^2+y^2+z^2)在(1,1,0)的線性化方程式L(x,y)為何?
9. xe^v+sin(xy)+y-ln(2)=0在(0,ln(2))處的dy/dx為何?
10.若h(x,y,z)=e^(x+y)cos(z),則在(0,0,π/6)處的梯度為何?
11. 若h(x,y,z)=ln(x^2+y^2-1)+y+6z,則在p[o](1,1,0)處增加最快的方向為何?
12.承上題,其最大導數值為何?
13. 若定義域為由xy平面上x軸、直線y=x , x=1所圍的三角形,則由曲面z=3-x-y
與此區域所圍的體積為何?
14.求曲線r^2=4cos(2θ)所圍的面積為何?
15.若D為曲面z=x^2+3y^2與z=8-x^2-y^2所圍的區域,則其體積為何?
16. 由四頂點(0,0,0), (1,1,0), (0,1,0), 以及(0,1,1)所為的四面體D, 對F(x,y,z)的三重積分方程式為何?
禮拜一要交!!感謝!!
若看不懂題目可以到http://www.mathway.com/problem.aspx?p=calculus
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