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Prove that the function , is continuous at but not differentiable.
Prove that the function $f(x) = |x - 1|, x \in \mathbb{R}$, is continuous at $x = 1$ but not differentiable.
Given: $f(x) = |x - 1|, x \in \mathbb{R}$
To show: $f(x)$ is continuous at $x = 1$ but not differentiable
Answer
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From ISC 2018 Specimen Mathematics Paper 1, question 5(a).