Example 3 - Discuss continuity of f(x) = |x| at x = 0 - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 3 Discuss the continuity of the function f given by 𝑓(𝑥) = | 𝑥 | 𝑎𝑡 𝑥 = 0. 𝑓(𝑥) = |𝑥| 𝑓﷐𝑥﷯= ﷐﷐−𝑥, 𝑖𝑓 𝑥<0﷮𝑥, 𝑖𝑓 𝑥 ≥0﷯﷯ f is continuous at 𝑥 = 0 if L.H.L = R.H.L = 𝑓(0) i.e. ﷐lim﷮x→﷐0﷮−﷯﷯ 𝑓﷐𝑥﷯=﷐lim﷮x→﷐0﷮+﷯﷯ 𝑓﷐𝑥﷯=𝑓(0) So, L.H.L = R.H.L & 𝑓(0) = |0| = 0. Hence, ﷐lim﷮x→﷐0﷮−﷯﷯ 𝑓﷐𝑥﷯=﷐lim﷮x→﷐0﷮+﷯﷯ 𝑓﷐𝑥﷯=𝑓(0) ∴ f is continuous at 𝒙 = 𝟎

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