Multivariable Calculus

  • Thread starter psycho81
  • Start date
  • #1
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Homework Statement


Define f : R2 -> R by

f (x, y) =

x²y
x4+y2 (x, y) ≠ (0, 0)

0 (x, y) = (0, 0).


(i)What value does f (x, y) take on the coordinate axes?

(ii) Define g : R -> R2 by

g(t) =

( t )
( kt )

k is an arbitrary nonzero constant. Describe the image of g. Calculate g(t) = f  g(t) . Is
g(t) continuous?

(iii) Define g1 : R -> R2 by

g1(t) =

( t )
( t^2 )


Calculate h(t) = f  g1(t). Also calculate lim t->0 h(t) for t ≠ 0. Explain clearly what
you have found out about the function h(t). Also explain what your calculations tell you
about the function f (x, y).


Homework Equations





The Attempt at a Solution



do i just set z=0 for (i)

help with the other parts would be good too.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
for i) i think it means set x=0, then seprately set y=0 and consider teh values the function takes in each case
 

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