# How do you prove that the function f(x) = (x + 2x^3)^4 is continuous at x=-1?

Since $f \left(- 1\right) = \lim x \to - 1 \left(f \left(x\right)\right)$ therefore f(x) is continuous at x = -1
$1. f \left(- 1\right) = {\left(- 1 + 2 {\left(- 1\right)}^{3}\right)}^{4} = {\left(- 1 - 2\right)}^{4} = {\left(- 3\right)}^{4} = 81$
$2. \lim x \to - 1 \left[{\left(x + 2 {x}^{3}\right)}^{4}\right] \to {\left(- 1 + 2 {\left(- 1\right)}^{3}\right)}^{4} = {\left(- 1 - 2\right)}^{4} = {\left(- 3\right)}^{4} = 81$
$3.$ Since $f \left(- 1\right)$ = $\lim x \to - 1 f \left(x\right)$ therefore f(x) is continuous at x = -1