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Show that f(x) = |x – 5| is continuous but not differentiable at x = 5.

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Show that f(x) = |x – 5| is continuous but not differentiable at x = 5.

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Consider left hand limit at x = 5

It can be written as

Here Lf' ≠ Rf'

Therefore, the function is continuous but not differentiable at x = 5.

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