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+1 vote
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in Continuity and Differentiability by (42.5k points)
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Show that  \(f(x) = \begin{cases} x , & \quad \text{if } x≠0; \text{}\\ 1, & \quad \text{if } x=0\text{} \end{cases}\)   is continuous at each point except 0.

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Given function is  \(f(x) = \begin{cases} x , & \quad \text{if } x≠0; \text{}\\ 1, & \quad \text{if } x=0\text{} \end{cases}\) 

Left hand limit at x = 0

f(x) = x for other values of x expect 0 f(x) = 1,2,3,4… 

Therefore, 

f(x) is not continuous everywhere expect at x = 0

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