Example 14 - Show that every polynomial function is continuous - Examples

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Example 14 Show that every polynomial function is continuous Let 𝑓﷐𝑥﷯=﷐𝑎﷮0﷯﷐𝑥﷮0﷯+﷐𝑎﷮1﷯𝑥+﷐𝑎﷮1﷯﷐𝑥﷮2﷯𝑡…… +﷐𝑎﷮𝑛﷯﷐𝑥﷮𝑛﷯ 𝑛∈𝒁 be a polynomial function Polynomial function is satisfied for every real number We know that A function is continuous at 𝑥 = 𝑐 if ﷐lim﷮x→𝑐﷯ 𝑓﷐𝑥﷯= 𝑓﷐𝑐﷯ Let c be any Real number Checking for continuity at x = c Thus ﷐lim﷮x→𝑐﷯ 𝑓﷐𝑥﷯ = 𝑓﷐𝑐﷯ Therefore 𝑓﷐𝑥﷯ is continuous for all Real numbers ⇒ So every polynomial function is continuous.

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