Continuity and Differentiability — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Show that every polynomial function is continuous.
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Answer
Recall that a function p is a polynomial function if it is defined by $p(x) = a_0 + a_1 x + ... + a_n x^n$ for some natural number $n, a_n \neq 0$ and $a_i \in R$. Clearly this function is defined for every real number. For a fixed real number c, we have
$\mathop {\lim }\limits_{x \to c} p(x)= p (c)$
By definition,$p$ is continuous at $c$. Since $c$ is any real number, $p$ is continuous at every real number and hence $p$ is a continuous function.
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