Given a function f : Rm → R" which is continuous on Rm and v E Rm \ {0}. Prove that the function fº : R → R" defined by fº(t) = f(tv) is continuous on R. Define f : R2 → R by letting (a) (b) (y? – a)? (y4 + x²) f (x, y) if (x, y) # (0,0), and f(0,0) = 1. Prove that f" is continuous on R for all v E R² \ {(0,0)}, but that f itself is discon- tinuous at (0,0) (relative to R²).

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