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Math Help - Limits of 2 Variables

  1. #1
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    Limits of 2 Variables

    lim ( cos(x)-1 + (x^2)/2 ) / (x^4 + y^4)
    (x,y) - (0,0)


    To evaluate this limit do i use L'Hospital's rule a few times to get it down to a solution or am i reading into it too much and is easier way?


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  2. #2
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    Quote Originally Posted by monster View Post
    lim ( cos(x)-1 + (x^2)/2 ) / (x^4 + y^4)
    (x,y) - (0,0)


    To evaluate this limit do i use L'Hospital's rule a few times to get it down to a solution or am i reading into it too much and is easier way?


    Cheers
    First approach (0,0) from different directions. Along the y axis (x=0) then

    \lim_{y \to 0} \frac{0}{y^4} = 0.

    Then along the x axis (y=0) then

    \lim_{x \to 0} \frac{ \cos x - 1 + \frac{1}{2}x^2}{x^4} (use L'Hopital's rule on this one)
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