## anonymous 5 years ago if f(x) = x^{3} +8 / X+2 is continuous at x= -2, then f(-2)=? help?

1. anonymous

If it was continuous, then the limit as x tended to -2 of f(x) would be equal to f(-2)

2. anonymous

can you demonstrate?

3. anonymous

Just take that limit. Note that x^3+8 can be written as (x+2) (x^2-2x+4)

4. anonymous

Thank you sooo much. Can I bother you with one more problem?

5. anonymous

It's not a bother.

6. anonymous

$\lim_{n \rightarrow 0} \sin 3x/ \sin2x$

7. anonymous

chaguanas gave the method the previous time you asked it. Essentially divide top and bottom by 3x. But for the numerator, factor out a value such that you get sin(2x)/2x and we know that lim x->0 sin(nx)/n=0

8. anonymous

For the denominator i mean

9. anonymous

Xavier, I'm still trying to figure out how you changed x^3+8 to (x+2) (x^2-2x+4)

10. anonymous

I prayed that (x+2) is a factor and divided.

11. anonymous