本次香港代写主要为数学的限时测试
第一章
1.确定功能是否
f(x; y)=
8
<
:
pxy + 1 1
y
x = 0和y = 0和xy 1;
0(x; y)=(0; 0):
是否在(0; 0)处连续。证明你的结果。
2.确定功能是否
f(x; y)=
8
<
:
2×2
ÿ
x4 + y2
[x; y)=(0; 0)
0(x; y)=(0; 0):
是否在(0; 0)处连续。证明你的结果。
3.找到函数的绝对最小值和绝对最大值
f(x; y)=
封闭的半磁盘上的px2 + y2 2x + 2 R = f(x; y):x2
+ y2
</ s> </ s> </ s> </ s> </ s>
4; y 0克。
4.找到以下函数的绝对最小值和绝对最大值
f(x; y)= x2
y(4 x y)在以x轴,y轴和
线x + y = 6。
5.球体每个点的温度x2
+ y2
+ z2
= 11由
函数T(x; y; z)= 20 + 2x + 2y + z2
。找到最高和最低
给定球体x2的交点上的温度
+ y2
+ z2
= 11并且
平面x + y + z = 3。
6.使用牛顿-拉夫森方法的一个迭代进行初始猜测(1; 1)
解决线性方程组
(
2倍
+ 4年2
9 = 0
18岁14×2
+ 45 = 0
:
7.找到函数的所有临界点w = x3
+ y3
12x 3y + 20。还可以阻止-
挖掘临界点的性质(相对最大值,相对最小值
或鞍点)。
8.找到函数f(x; y)=的所有相对和绝对最大值和最小值
2倍
22
+ 2x + 4y + 2在闭合的第一个象限x 0,y 0
9.令w = x2
e2y
cos(3z)。在点(1; ln 2; 0)上找到dw = dt的值
曲线x = cos t,y = ln(t + 2),z = t
10.找出f(x; y)= xy + 2x ln(x2
y)在开放的第一个象限中
x> 0和y>0。还要确定此临界点的性质(相对
最大值,相对最小值或鞍点)。
11.找到并分类所有对于f(x; y)= 3×2的临界点
y + y3
3×2
3年2
+2。
12.确定功能是否
Chapter One
1. Determine whether the function
f(x; y) =
8
<
:
pxy + 1 1
xy
x = 0 and y = 0 and xy 1;
0 (x; y) = (0; 0):
is continuous at (0; 0) or not. Prove your result.
2. Determine whether the function
f(x; y) =
8
<
:
2×2
y
x4 + y2
(x; y) = (0; 0)
0 (x; y) = (0; 0):
is continuous at (0; 0) or not. Prove your result.
3. Find the absolute minimum and absolute maximum value of the function
f(x; y) =
px2 + y2 2x + 2 on the closed half disk R = f(x; y) : x2
+ y2
4; y 0g.
4. Find the absolute minimum and absolute maximum value of the function for
f(x; y) = x2
y(4 x y) in the closed region bounded by x axis, y axis and
the line x + y = 6.
5. The temperature at each point of the sphere x2
+ y2
+ z2
= 11 is given by
the function T(x; y; z) = 20 + 2x + 2y + z2
. Find the highest and lowest
temperature on the intersection of the given sphere x2
+y2
+z2
= 11 and the
plane x + y + z = 3.
6. Using ONE iteration of Newton-Raphson’s method with initial guess (1; 1)
to solve the system of linear equations
(
x2
+ 4y2
9 = 0
18y 14×2
+ 45 = 0
:
7. Find all critical points of the function w = x3
+y3
12x 3y+20. Also deter-
mine the nature of the critical points (relative maximum, relative minimum
or saddle point).
8. Find all relative and absolute maxima and minima of the function f(x; y) =
x2
y2
+ 2x + 4y + 2 on the closed rst quadrant x 0, y 0.
9. Let w = x2
e2y
cos (3z). Find the value of dw=dt at the point (1; ln 2; 0) on the
curve x = cos t, y = ln(t + 2), z = t.
10. Find the critical point of f(x; y) = xy+2x ln(x2
y) in the open rst quadrant
x > 0 and y > 0. Also determine the nature of this critical point (relative
maximum, relative minimum or saddle point).
11. Find and classify all the critical points for f(x; y) = 3×2
y+y3
3×2
3y2
+2.
12. Determine whether the function