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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).