Question

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

Answer 1

Since `f(-1) = lim x->-1 (f(x))` therefore f(x) is continuous at x = -1

Explanation:

`1. f(-1)=(-1+2(-1)^3)^4 =(-1-2)^4=(-3)^4=81`
`2. lim x->-1 [(x+2x^3)^4]->(-1+2(-1)^3)^4 =(-1-2)^4=(-3)^4=81`
`3.` Since `f(-1)` = `lim x->-1 f(x)` therefore f(x) is continuous at x = -1