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in Continuity and Differentiability by (42.5k points)
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Show that ƒ(x) = x3 is continuous as well as differentiable at x=3

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Given: f(x) = x3 

If a function is differentiable at a point, it is necessarily continuous at that point. 

Left hand derivative (LHD) at x = 3

LHD = RHD T

herefore, f(x) is differentiable at x = 3.

\(\lim\limits_{x \to 3}\) f(x) = \(\lim\limits_{x \to 3}\) x3 = 33 = 27

Also, f(3) =27 

Therefore, f(x) is also continuous at x = 3.

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