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

Question

anonymous · Answer

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

anonymous · Answer

can you demonstrate?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

It's not a bother.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

For the denominator i mean

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Oh, prayer answered.