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Thread: How to solve this limit? limit, (x,y)=>(0,0), of sin(xy) / (xy)

  1. #1
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    How to solve this limit? limit, (x,y)=>(0,0), of sin(xy) / (xy)

    Hello, can someone help me with this exercise please ?

    I have to study this limit when x and y tends to (0,0) [tex] f(x,y) = sin(xy)/(xy) [/tex]

    Aproximating the limit I get that it exists. However, I don't know how to calculate it.

  2. #2
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by Anto View Post
    Hello, can someone help me with this exercise please ?

    I have to study this limit when x and y tends to (0,0) [tex] f(x,y) = sin(xy)/(xy) [/tex]

    Aproximating the limit I get that it exists. However, I don't know how to calculate it.
    Are you able to refer at all to the basic trig limit you learned back in first-semester calculus? Namely:

    . . . . .[tex]\displaystyle \lim_{\theta\, \rightarrow\, 0}\, \dfrac{\sin(\theta)}{\theta}\, =\, 1[/tex]

    I think this is sufficient (rename "xy" as "z", say, and let z goes to zero), but you can review another (much more advanced) argument here.

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