## Calculus 8th Edition

The function is continuous $a = -1.$
By theorem 8 we can write $\lim\limits_{x \to -1} (x + 2x^{3})^{4}$ as $(\lim\limits_{x \to -1} (x + 2x^{3}))^{4}$ This is a polynomial so its limit can be evaluated by substitution. Because it is evaluated by substitution, the value of the function at -1 is equal to the value of the limit at -1 which means that it is continuous.