Results 1 to 2 of 2

Math Help - Difference quotients

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    80

    Difference quotients

    Here's the question:

    "Use difference quotients with delta(x)=0.1 and delta(y)=0.1 to estimate fx(1,3) and fy(1,3) where f(x,y)=e^(-x)sin(y)."

    My work so far:

    I know that to begin with, you have to find the partial derivative with respect to both x and y and then plug the point (1,3) into this equation. So for x the derivative would be -1e^(-x)sin(y) and for y the derivative would be e^(-x)cos(y). Now, what do I do after I plug the point (1,3) into these two equations? Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2009
    Posts
    226
    Here is how the difference quotient is used to define the first partial derivatives of f(x,y) at (1,3).

    f_x(1,3) = \lim_{\Delta x \to 0}\frac{f(1 + \Delta x,3) - f(1,3)}{\Delta x} \approx \frac{f(1 + 0.1,3) - f(1,3)}{0.1} = \frac{e^{-(1 + 0.1)}\sin{3} - e^{-1}\sin{3}}{0.1} = \frac{e^{-1.01}\sin{3} - e^{-1}\sin{3}}{0.1}

    f_y(1,3) = \lim_{\Delta y \to 0}\frac{f(1,3 + \Delta y) - f(1,3)}{\Delta y} \approx \frac{f(1,3 + 0.1) - f(1,3)}{0.1} = \frac{e^{-1}\sin{3 + 0.1} - e^{-1}\sin{3}}{0.1} = \frac{e^{-1}\sin{3.1} - e^{-1}\sin{3}}{0.1}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. evaluating difference quotients
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: October 1st 2009, 06:02 PM
  2. Help!! Difference Quotients.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 28th 2009, 01:45 PM
  3. horray for difference quotients
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: August 31st 2008, 11:30 PM
  4. Difference Quotients
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 29th 2008, 02:24 PM
  5. Difference Quotients
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 20th 2007, 04:56 PM

Search Tags


/mathhelpforum @mathhelpforum