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Example 9 - Discuss continuity of f(x) = 1/x - Chapter 5 - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 9 Discuss the continuity of the function f defined by 𝑓 (𝑥) = ﷐1﷮𝑥﷯ , 𝑥 ≠ 0. Given 𝑓 (𝑥) = ﷐1﷮𝑥﷯ At 𝑥 = 0 𝑓 (𝑥) = ﷐1﷮𝑥﷯ 𝑓 (0) = ﷐1﷮0﷯ = 𕔴 Hence 𝑓 (𝑥) is not defined at 𝑥 = 0 By definition, 𝑓 (𝑥) = ﷐1﷮𝑥﷯ , 𝑥 ≠ 0. So, we check for continuity at all points except 0. Let c be any real number except 0. f is continuous at 𝑥 =𝑐 if , ﷐lim﷮x→𝑐﷯ 𝑓﷐𝑥﷯=𝑓﷐𝑐﷯ Thus ﷐lim﷮x→𝑐﷯ 𝑓﷐𝑥﷯=𝑓﷐𝑐﷯ ⇒ f is continuous at 𝑥 =𝑐 (Except 0) f is not continuous for all 𝒙 ∈𝐑−{𝟎}

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