1) Use the transformation x=u and y=uv where R is the region bounded by the triangle with vertices (1,1),(7,4) and (1,2)

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1 Use The Transformation X U And Y Uv Where R Is The Region Bounded By The Triangle With Vertices 1 1 7 4 And 1 2 1 (31.21 KiB) Viewed 73 times

1) Use the transformation x=u and y=uv where R is the region bounded by the triangle with vertices (1,1),(7,4) and (1,2). 2) Use the transformation u=y and v=1−y2x​ where R is the region bounded by the curves x+y2=1 and x+9y2=9. For each of the above problems, complete the following steps, showing all relevant work for another student to follow: a) Sketch and shade region R in the xy-plane. b) Label each of your curve segments that bound region R with their equation and domain. c) Find the image of R in uv-coordinates. (That is to say, show appropriate work to find the boundaries of set S in the uv-coordinate system.) d) Sketch and shade set S in the uv-plane. 3) Use the transformation x=u−v and y=u+v where S is the set bounded by the triangle with vertices (0,0),(1,1) and (2,0). 4) Use the transformation u=xy and v=y/x where S is the set bounded by the curves u=1,u=4,v=1 and v=4. For each of the above problems, complete the following steps, showing all relevant work for another student to follow: a) Sketch and shade set S in the uv-plane. b) Label each of your curve segments that bound set S with their equation and domains. c) Find the pre-image of S in xy-coordinates. (That is to say, show appropriate work to find the boundaries of set R in the xy-coordinate system.) d) Sketch and shade set R in the xy-plane.