Consider the lim as x,y approaches (0,0) (x^2+y^2)/xy Consider the lim as x,y ap

Question

Consider the lim as x,y approaches (0,0) (x^2+y^2)/xy

Consider the lim as x,y approaches (0,0) (x^2+y^2)/xy 6. Consider lim (x,y) right arrow (0,0) x^2+y^2/xy (see figure). (a) Determine (if possible) the limit along any line of the form y = ax. (Assume a not integral 0. If an answer does not exist, enter DNE.) (b) Determine (if possible) the limit along the parabola y = x^2. (If an answer does not exist, enter DNE.) (c) Does the limit exist? Explain. Yes, the limit exists. The limit Is the same regardless of which path is taken. No, the limit does not exist. Different paths result in different limits. Submit Answer Save Progress

Explanation / Answer

1)limx->0 (x^2 +(ax)^2)/x*ax

=limx->0 (x^2(1+a^2)/ax^2

=(1+a^2)/a

2)limx->0 (x^2 +(x^2)^2)/x*x^2

=limx->0 ((1+x^2)/x)

l hospital rule differentiate numerator ,denominator wrt x

limx->0 ((2x)/1)

=2*0

=0

3)no, limit doesnot exist ,different paths gives different limits

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