How do you prove that the function f(x) = (x + 2x^3)^4 is continuous at x=-1? Calculus Limits Definition of Continuity at a Point 1 Answer Bdub 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 Answer link Related questions What are the three conditions for continuity at a point? What is continuity at a point? What is the definition of continuity at a point? What does continuous at a point mean? What makes a function continuous at a point? How do you find the points of continuity and the points of discontinuity for a function? What does continuity mean? How do you use continuity to evaluate the limit arctan(x^2-4)/(3x^2-6x)? How do you find the points of continuity of a function? How do you find the continuity of a function on a closed interval? See all questions in Definition of Continuity at a Point Impact of this question 4581 views around the world You can reuse this answer Creative Commons License