Results 1 to 3 of 3

Math Help - Surface defined on the domain?

  1. #1
    Junior Member
    Joined
    Mar 2011
    Posts
    27

    Surface defined on the domain?

    "Let S be the surface z = e^(x+y) - 2, defined on the domain D = {(x,y) ∈ ℝ^2 | x ≥ 0 and y ≥ 0}. What is the minimal value of z for points on S?"

    With this question, I thought that since both the x- and y-values need to be greater than zero for the domain, then obtaining the minimal value would simply mean subbing 0 into the equation. I did that, and got the answer, -1. (Which also matches up as being the correct answer to the question). So, I just basically want to know was what I did to get the answer correct or is there some other way you get the answer? (As, I may be wrong but it just seems that it was a bit of a straightforward and simple approach with getting the answer.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member abhishekkgp's Avatar
    Joined
    Jan 2011
    From
    India
    Posts
    495
    Thanks
    1
    what you did is correct. it can be explained as follows:
    1) the value of z completely depends on the value of x+y.
    2)the lower the value of x+y the lower the value of z.
    3) the least value of x+y available in D is 0.
    so e^0-2 is the answer.

    Here the situation was fairly simple so we could use the above reasoning. In general such problems are solved using multivariate calculus.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    We have

    -1\leq e^{x+y}-2\Leftrightarrow 1\leq e^{x+y}

    The second inequality is true for all x\geq 0,y\geq 0 so, -1 is a lower bound for

    z=f(x,y)=e^{x+y}-2

    On the other hand we get that bound: f(0,0)=-1 .


    Edited: Sorry, Ididn't see the previous post.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 17th 2011, 01:46 AM
  2. Replies: 2
    Last Post: April 25th 2010, 08:22 AM
  3. Replies: 2
    Last Post: August 5th 2009, 10:20 AM
  4. Calculate the surface area of the surface
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 26th 2009, 04:03 AM
  5. Help finding surface area of a surface
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 3rd 2008, 04:11 PM

Search Tags


/mathhelpforum @mathhelpforum