Use polar coordinates to find the limit

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Faka
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Hi!
Is there somebody, who can help me with this exercise:
"Use polar coordinates to find the limit. [If (r, θ ) are polar coordinates of the point (x,y) with r ≥ 0, note that r --> 0+ as (x,y) --> (0,0)]
 
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  • Limit expression: lim as (x,y) approaches (0,0) of (x^3 + y^3)/(x^2 + y^2).
    Limit.jpg
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I've done this so far. I do not know how to determine what the limit is.
 
Attachments
  • Handwritten-style derivation: limit as (x,y) approaches (0,0) of (x^3+y^3)/(x^2+y^2), converted to polar coordinates to become limit as r approaches 0+ of r(cos^3(θ)+sin^3(θ)).
    Limit 2.jpg
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Looks like a continuous function of r to be, what are the limits of continuous functions?
 
I hope this is right :smile:
 
Attachments
  • Handwritten-style limit derivation converting lim (x,y)->(0,0) of (x^3+y^3)/(x^2+y^2) to polar coordinates, reaching lim r->0+ of r times (cos^3 theta + sin^3 theta), which equals 0.
    Limit 3.jpg
    8.6 KB · Views: 1,283