1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Approximation

  1. Nov 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f(x,y) = [itex](xe^y)^8[/itex]

    i) Find

    [itex]\frac{∂f}{∂x}[/itex] [itex]\frac{∂f}{∂y}[/itex] [itex]\frac{∂^2f}{∂x^2}[/itex]

    ii) Using a tangent plane of f(x,y) find an approximate value of (0.98e^0.01)^8

    2. Relevant equations
    3. The attempt at a solution

    [itex]\frac{∂f}{∂x}[/itex] =[itex] 8e^{8y}x^{7}[/itex]

    [itex]\frac{∂f}{∂y}[/itex] = [itex] 8x^{8}e^{8y}[/itex]

    [itex]\frac{∂^2f}{∂x^2}[/itex] = [itex] 56e^{8y}x^{6}[/itex]

    ii) I have done many questions on finding linear approximations but I have always had a function, a point to evaluate the function at and points to approximate it at.

    In this I have the function Let f(x,y) = [itex](xe^y)^8[/itex] and want to use it to approximate f(0.98,0.01) but I'm not sure at what point I should evaluate it at.

    Can anyone help out?
  2. jcsd
  3. Nov 3, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Since .98 is reasonably close to 1 and 0.01 close to 0, I think x= 1, y= 0 would be a good try.
  4. Nov 4, 2011 #3
    Was leaning towards that, just wanted to make sure.

    That all worked out nicely, thanks for your advice =D
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Linear Approximation
  1. Linear approximation (Replies: 4)

  2. Linear approximation (Replies: 1)

  3. Linear Approximation (Replies: 4)

  4. Linear Approximations (Replies: 3)