- #1
jameszy7
- 2
- 0
a) The two surfaces defined by xz^2 + 2yz +xy^2 = 4, 2x - 7y - 3z = 2 intersect in a curve S. Find the tangent line and normal plane to S at the point (3,1,-1).
b) Sketch the graphs of y = x^m and y = x^n where m and n are positive integers and x >= 0 . Find the area of the region enclosed between them. Is your answer valid for m>n or m <n ?
c) Let F = e^x i + 2ye^x j + e^2y^^2 k
(i,j and k are not part of the power)
Verify the divergence theorem over the box-like region described by
0<=x<=1, 0<=y<=2, 0<=z<=3.
d) Evaluate the triple integral
\int_{2}^{0} \int_{2x}^{0} \int_{y}^{0} xe^z dzdydx
Sorry if this looks messy, its my first post here :D
b) Sketch the graphs of y = x^m and y = x^n where m and n are positive integers and x >= 0 . Find the area of the region enclosed between them. Is your answer valid for m>n or m <n ?
c) Let F = e^x i + 2ye^x j + e^2y^^2 k
(i,j and k are not part of the power)
Verify the divergence theorem over the box-like region described by
0<=x<=1, 0<=y<=2, 0<=z<=3.
d) Evaluate the triple integral
\int_{2}^{0} \int_{2x}^{0} \int_{y}^{0} xe^z dzdydx
Sorry if this looks messy, its my first post here :D