Let $x_n \rightarrow x$ and let $p(t)$ be a polynomial. Show that $p(x_n) \rightarrow p(x)$

Asked Oct 03 '19 at 21:17

Active Oct 03 '19 at 23:41

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I want to solve the proof by using mathematical induction. I'm just not exactly sure of how I should start, like how should I do the base case?

edited Oct 03 '19 at 23:41

azif00

asked Oct 03 '19 at 21:17

Claire

2

This is asking to prove polynomials are continuous, so this link might be helpful: https://math.stackexchange.com/questions/732115/how-can-i-prove-that-a-polynomial-with-degree-n-is-continuous-everywhere-in – 79037662 Oct 03 '19 at 21:19
1

The proof depends on what is given. Can we use the fact that if f and g are convergent sequences, then f*g is convergent? – Spencer Kraisler Oct 04 '19 at 03:27

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