Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.

Question

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.

F(x) = (x+3x^4)^3, a = -1

Answer 1

First of all F(x) is a polynomial of degree 12.

Polynomials are continuous everywhere on the real line, because each term in the polynomial is continuous and the limit of a sum is the sum of the limits.

Continuity means that lim x->a f(x)=f(a); that means that you can substitute the point to which x is tending into the function to evaluate the limit.