Example 14 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at August 11, 2026 by Teachoo
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Chapter 5 Class 12 Continuity and Differentiability
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Example 14 Show that every polynomial function is continuousLet š(š)=š_š+š_š š+š_š š^š+ ā¦ +š_š š^š šāš be a polynomial function Since Polynomial function is valid for every real number We prove continuity of Polynomial Function at any point c Let c be any real number f(x) is continuous at š„ = š if (š„š¢š¦)ā¬(š±āš) š(š)= š(š) L.H.S (š„š¢š¦)ā¬(š±āš) š(š) = limā¬(xāš) " " (š_0+š_1 š„+ ā¦ +š_š š„^š ) Putting x = c = š_0+š_1 š+ ā¦ +š_š š^š R.H.S š(š) = š_0+š_1 š+ ā¦ +š_š š^š Since, L.H.S = R.H.S ā“ Function is continuous at x = c Thus, we can write that f is continuous for all š āš i.e. Every polynomial function is continuous.
