Evaluate the limit along the paths given, and then state why these results show the given limit does not exist. lim (x,y)?(0,0) (x+y)² / (x² + y²). (a) Along the path y = x. (b) Along the path y = -x.
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Step 1:** Evaluate the limit along the path y = x: Substitute y = x into the given function: lim (xtw)z (xy)-(0,0) 2+y^2 = lim (x,x)z (x*x)-(0,0) 2+x^2 = lim (x,x)z x^2-0 2+x^2 = lim (x,x)z x^2 2+x^2 = 1/2 ** Show more…
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