Find the parameterization of the surface area given by #z = x^2 - 2x + y^2#?

A possible parameterization is # r(p, q) = (1 + p * cos(q), p sin(q), p^2 - 1)#, but why?

Answer 1

Isabella Ackerman

Looking at your suggested parameterization, rather than actually finding one:

Looking at individual terms of #z(x,y)= x^2 - 2x + y^2# in terms of the parameterization:

#bbbA + bbbB + bbbC = 1 + cancel(2 p cosq) + p^2 cos^2 q -2 - cancel(2 p cosq) + p^2 sin^2q #

#= p^2 (cos^2 q + sin^2q) -1#

#= p^2 -1 color(blue)( = z(p,q))#

So that seems to work

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Trending questions

Not the question you need?

HIX Tutor

Solve ANY homework problem with a smart AI

98% accuracy study help
Covers math, physics, chemistry, biology, and more
Step-by-step, in-depth guides
Readily available 24/7

Find the parameterization of the surface area given by #z = x^2 - 2x + y^2#?

A possible parameterization is # **r**(p, q) = (1 + p * cos(q), p sin(q), p^2 - 1)#, but why?

A possible parameterization is # r(p, q) = (1 + p * cos(q), p sin(q), p^2 - 1)#, but why?