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Examine whether the function f given by f(x)=x^(3)is continuous at x =0

Answer»

Solution :The function is defined at the GIVEN point x =0 and its VALUE is 0.
CLEARLY, ` underset (xto0) lim f(x) = underset (x to 0) x^(3)= 0^(3) =0`
` underset( xto 0) f(x) =0 = f (0) `
Hence, f is CONTINOUS at x = 0


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