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# HWO4 11.1-11.3: Problem 6Previous ProblemProblem ListNext Problempoint) In this problem we show that the functionIxl _y f(xY) = x2 + ydoos not have Ilmit as (x,Y)(0...

## Question

###### HWO4 11.1-11.3: Problem 6Previous ProblemProblem ListNext Problempoint) In this problem we show that the functionIxl _y f(xY) = x2 + ydoos not have Ilmit as (x,Y)(0.0)(a) Suppose that we consider (x, Tx? _ y lim (521')-(Q,0) +>along the curve2x" . Find the Iimit in this case:(b) Now consider (x,Y)(0,0) along tha curve3x2 Find Ihe Iimit in this case:lim14_ (1,Jr-)-+(0.0) x + y(c) Note that the results from (a) and (b) indicate that has no limit as (X,Y)(0,0) (be sure You can explain

HWO4 11.1-11.3: Problem 6 Previous Problem Problem List Next Problem point) In this problem we show that the function Ixl _y f(xY) = x2 + y doos not have Ilmit as (x,Y) (0.0) (a) Suppose that we consider (x, Tx? _ y lim (521')-(Q,0) +> along the curve 2x" . Find the Iimit in this case: (b) Now consider (x,Y) (0,0) along tha curve 3x2 Find Ihe Iimit in this case: lim 14_ (1,Jr-)-+(0.0) x + y (c) Note that the results from (a) and (b) indicate that has no limit as (X,Y) (0,0) (be sure You can explain whyl): To show this more generally; consider (x, Y) (0,0) along the curve mx" , for arbitrary m . Find the Ilmit In this caso: Jxl _ y lim (I,m" )-+(0,0) x2 +y (Be sure that you can oxplain how this result also Indlcatos that has nO limit as (,P) (0,0).

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