Calculus: Use limits to show that the function is continuous at the given number a.

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+2x^3)^4, a=-1.

PLEASE HELP ME WITH THIS PROBLEM. THANK YOU!

If f(x) is continuous at x = a, then:
lim (x-->a-) f(x) = lim (x-->a+) f(x) = f(a).

Since:
(i) lim (x-->-1-) f(x)
= lim (x-->-1-) (x + 2x^3)^4
= [-1 + 2(-1)]^4
= 81
(ii) lim (x-->-1+) f(x)
= lim (x-->-1+) (x + 2x^3)^4
= [-1 + 2(-1)]^4
= 81
(iii) f(-1) = [-1 + 2(-1)]^4 = 81
==> lim (x-->-1-) f(x) = lim (x-->-1+) f(x) = f(-1),

we see that f(x) is continuous at x = -1.

I hope this helps!

the limit does not exist