If $p$ is a polynomial, then $\lim_{x \to a} p(x)$
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.. + a_1x + a_0, where a_n, a_{n-1}, ..., a_1, a_0 are constants and n is a non-negative integer. Show more…
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If $p$ is a polynomial, show that $\lim _{x \rightarrow a} p(x)=p(a)$
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If p is a polynomial, show that lim p(x) = p(a). Since p(x) is a polynomial, p(x) = a0 + a1x + a2x^2 + ... + anx^n. Thus, by the limit laws, lim p(x) = lim (a0 + a1x + a2x^2 + ... + anx^n) = a0 + a1lim x + a2lim x^2 + ... + anlim x^n = p(a). Thus, for any polynomial p, lim p(x) = p(a).
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