Find a vector-valued function whose graph is the indicated surface. N

vousetmoiec

vousetmoiec

Answered question

2021-11-12

Find a vector-valued function whose graph is the indicated surface.
The cylinder 4x2+y2=16

Answer & Explanation

Helen Rodriguez

Helen Rodriguez

Beginner2021-11-13Added 9 answers

Step 1
In polar coordinates, x=rcosθ, y=rsinθ
Using this rule, using appropriate substitutions:
x=2cosu, y=4sinu
Step 2
Considering z=v, the vector form is given by:
r(u,v)=2cosui+4sinuj+vk
Step 3
Answer:
r(u,v)=2cosui+4sinuj+vk

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