Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




Not registered yet?

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno

Go back

Topic review (newest first)

2005-10-12 08:57:55

I am stuck in a some questions and I have no idea how to do them. If someone can help me it will be very much appreciated:

(1) For any x, y, prove that absolute value xy<= 1/2(x^2+ y^2)
suppose f(x,y)= x^2y^2/ x^2+y^2 . For any E(epsilon)>0 find a d(delta)>
0 such that if 0<(x^2+ y^2)^1/2 < d then absolute f(x,y) < E. Hence
prove tht f approaches a limit as (x,y) go to (0,0)

(2) For the function  f(x,y)= {x^2+y^2 for x,y both rational and it's 0
for anything otherwise.

determine wher f is continuous and wher it's discontinuous. Does f have
any partial derivative? Note, every neighbourhood in R^2 always
contains points with rational and points with irrational coordinates)

I'm really sorry for the trouble but i would really appreciate the

Board footer

Powered by FluxBB