Help with limits: Determine the value of "a" that would make the following function continuous:
h(x)={1. x^3 +a^3 if x

Question

Help with limits: Determine the value of "a" that would make the following function continuous:
h(x)={1.    x^3 +a^3  if    x<2     2. 4-2x      if    x is greater than or equal to 2

Answer choices:
a. -2
b. -1
c. 0
d. 2
e. cannot be determined 

I have no clue how to figure this out, and I am pretty sure it is very simple.

evoker · Answer

You need for the value at 2 to be the same for both pieces.

evoker · Answer

so you need x^3+a^3=4-2x   when x=2

stephy321 · Answer

@Evoler, would the answer be a. -2 because when plugged in, both sides of the function equal to 0?

stephy321 · Answer

@Evoker *

alt23345 · Answer

@stephy321 I got A as my answer as well.