how do I find the limit of the following two? 1. limit of xyz/(x^3+yz^2) as (x,y,z) goes to (0,0,0) 2. limit of (x+y)/(sqrt.(x^2+y^2)) as (x,y,z) goes to (0,0,0)
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Neither of these limits exist. For the first, try following the path $\displaystyle x = at, y= bt, z = ct$ and the second $\displaystyle y = mx, z=0$.
I made a simple mistake. The second one is as (x,y) goes to (0,0). Is the answer still the same?
Yes, just omit the $\displaystyle z$.
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