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!

Help with a simple limit

  1. May 13, 2009 #1
    f(x,y)=(sinx+siny)/(x+Y)
    as (x,y) approaches (0,0) and then for part II (pi/3,-pi/3)

    I know that sin(x+Y)/(x+y) would=1 by some simple tweaks. But in my problem, the 2 sins on the numerator are confusing me a little. Since x and y are approaching the same point on the first limit can i say x=y. and write f(x,y)=(sinx+sinx)/2x ?
     
  2. jcsd
  3. May 13, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    There is a trig identity that will let you express sin(x)+sin(y) in terms of sin((x+y)/2) and cos((x-y)/2), can you dig it up? Assuming x=y isn't going work for part II) anyway.
     
  4. May 13, 2009 #3

    Shooting Star

    User Avatar
    Homework Helper

    I think the teacher (or the book) wants you to use a formula for sinx+siny, which will give the answer directly.

    EDIT: Ooh, close finish with Dick...
     
  5. May 14, 2009 #4
    lol yeah forgot to check formulas. its sinX + sinY = 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ] and it will prob work with both parts ill check it tomorrow. Also, f(x,y) has a singularity on x+y. questions wants proof that it is/ it is not removable.
    Is it true that it is removable by plugging in a value at (0,0) i.e. finding a f(x,y) value that equals the lim f(x,y) as x and y approach 0.
    Is this rigorous enough? Thank you for the help!!!
     
  6. May 14, 2009 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, a singularity is removable if there is a well defined limit as you approach the singularity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help with a simple limit
  1. Simple Limit (Replies: 6)

  2. Simple limit (Replies: 2)

  3. Simple Limit (Replies: 3)

Loading...