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Let be a continuous real-valued function on the unit circle {x € R2 : |x| =1} such that

f (0, 1) = g(1, 0) = 0 and g(- x )= - g(x).

Define f: R2→R by

F (x) = {|x| . g (x/|x| x ≠0,

0 x = 0.

(a) If x € R2 and h: R →R is defined by h (t) = f (tx) show that h is differentiable.

(b). show that f is not differentiable at (0, 0) unless g = 0.

f (0, 1) = g(1, 0) = 0 and g(- x )= - g(x).

Define f: R2→R by

F (x) = {|x| . g (x/|x| x ≠0,

0 x = 0.

(a) If x € R2 and h: R →R is defined by h (t) = f (tx) show that h is differentiable.

(b). show that f is not differentiable at (0, 0) unless g = 0.

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