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

1 Answer
Mar 10, 2016

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