Multivariable Calculus: Surface Area and Change of Variables
Find the surface area of the surface given by z
=18−2x−3y over the triangle with vertices: (0,0), (2,3), (4,1).
Since this is not a type I or type II region, you will either need
to divide the region into two regions or use a change of variables.
x=(1/5)(u-2v) and y=(1/10)(3u-v) is a possible change of
variables.
I will upvote answers!
The paraboloid
z = 8 − x −
x2 −
2y2
intersects the plane x = 4 in a parabola. Find
parametric equations in terms of t for the tangent line to
this parabola at the point
(4, 2, −20).
(Enter your answer as a comma-separated list of equations. Let
x, y, and z be in terms of
t.)
Finding Surface Area In Exercises 43-46, find the area of the
surface given by z = f(x, y) that lies above the region R.
f(x,y)=4-x^2 R: triangle with vertices (-2,2),(0,0),(2,2)