Chapter 1 - Limits and Continuity - 1.5 Continuity - Exercises Set 1.5 - Page 99: 12

$$ f(x)=5 x^{4}-3 x+7 $$ is continuous everywhere

$$ f(x)=5 x^{4}-3 x+7 $$ we know from Theorem 1.2.3 that if $f(x)$ is a polynomial and $a$ is any real number, then $$ \lim _{x \rightarrow a} f(x)= f(a)$$ This shows that polynomials are continuous everywhere