Homework 3Due: Tuesday, November 27th1. Find the domain of the functionsa) fx,y)-32572-25b) f(x,y)-c) f(x,y)-36- 6x2 y22. Evaluate the limit using the properties of the limit:16-x2-y2-227xy2lim(x,y)-(2,3) X2 + y23. Verify the limit using the definition:7xy2(x,y)(0,0)%2 + y24. Discuss the continuity for:3x-x2+y2-95b) h(x,y)5. Find the partial derivatives for:4,2b) f(x,y)-e cos(xy2)6. Find the slope in the x-direction and in the y-direction of the surfacefix.y)-x2+ at the point (0,-1,2) using partial derivatives.

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Asked Dec 10, 2018
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Homework 3
Due: Tuesday, November 27th
1. Find the domain of the functions
a) fx,y)-32572-25
b) f(x,y)-
c) f(x,y)-36- 6x2 y2
2. Evaluate the limit using the properties of the limit:
16-x2-y2-22
7xy2
lim
(x,y)-(2,3) X2 + y2
3. Verify the limit using the definition:
7xy2
(x,y)
(0,0)%2 + y2
4. Discuss the continuity for:
3x-
x2+y2-9
5
b) h(x,y)
5. Find the partial derivatives for:
4,2
b) f(x,y)-e cos(xy2)
6. Find the slope in the x-direction and in the y-direction of the surface
fix.y)-x2+ at the point (0,-1,2) using partial derivatives.
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Homework 3 Due: Tuesday, November 27th 1. Find the domain of the functions a) fx,y)-32572-25 b) f(x,y)- c) f(x,y)-36- 6x2 y2 2. Evaluate the limit using the properties of the limit: 16-x2-y2-22 7xy2 lim (x,y)-(2,3) X2 + y2 3. Verify the limit using the definition: 7xy2 (x,y) (0,0)%2 + y2 4. Discuss the continuity for: 3x- x2+y2-9 5 b) h(x,y) 5. Find the partial derivatives for: 4,2 b) f(x,y)-e cos(xy2) 6. Find the slope in the x-direction and in the y-direction of the surface fix.y)-x2+ at the point (0,-1,2) using partial derivatives.

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Expert Answer

Step 1

1.

a)

Given

Here if x=0, f is undefined.

So domain of f is belonging to R2 except x≠0

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Step 2

Hence the domain is

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Step 3

 

b)

Given

Here if x2+y2+z2 = 16, f is undefined.

So to domain of f is belonging R2 except x...

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