Question

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

Answer 1

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

Answer 2

can you demonstrate?

Answer 3

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

Answer 4

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

Answer 5

It's not a bother.

Answer 6

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

Answer 7

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

Answer 8

For the denominator i mean

Answer 9

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

Answer 10

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

Answer 11

Oh, prayer answered.