2. Evaluate the limit using the properties of the limit: 2 7xy lim (x,y)-(2,3) x2 + y2 3. Verify the limit using the definition: 7xy2 lim x,y)-(0,0) χ 2 + y 2 4. Discuss the continuity for: a) g(x,y) x2+y2-9 b) h(x,y)-y-4 a) f(x,y) 4y+x4y2-5xy® 5 5. Find the partial derivatives for: b) f(x,y)-e"cos(xy2) 6. Find the slope in the x-direction and in the y-direction of the surface 2 -x2 +--+-at the point (0,-1,4) using partial derivatives. 4

Question

4

2. Evaluate the limit using the properties of the limit:
2
7xy
lim
(x,y)-(2,3) x2 + y2
3. Verify the limit using the definition:
7xy2
lim
x,y)-(0,0) χ 2 + y 2
4. Discuss the continuity for:
a) g(x,y) x2+y2-9
b) h(x,y)-y-4
a) f(x,y) 4y+x4y2-5xy®
5
5. Find the partial derivatives for:
b) f(x,y)-e"cos(xy2)
6. Find the slope in the x-direction and in the y-direction of the surface
2
-x2 +--+-at the point (0,-1,4) using partial derivatives.
4
Expand
Transcribed Image Text

2. Evaluate the limit using the properties of the limit: 2 7xy lim (x,y)-(2,3) x2 + y2 3. Verify the limit using the definition: 7xy2 lim x,y)-(0,0) χ 2 + y 2 4. Discuss the continuity for: a) g(x,y) x2+y2-9 b) h(x,y)-y-4 a) f(x,y) 4y+x4y2-5xy® 5 5. Find the partial derivatives for: b) f(x,y)-e"cos(xy2) 6. Find the slope in the x-direction and in the y-direction of the surface 2 -x2 +--+-at the point (0,-1,4) using partial derivatives. 4

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