anonymous
  • anonymous
if f(x) = x^{3} +8 / X+2 is continuous at x= -2, then f(-2)=? help?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
If it was continuous, then the limit as x tended to -2 of f(x) would be equal to f(-2)
anonymous
  • anonymous
can you demonstrate?
anonymous
  • anonymous
Just take that limit. Note that x^3+8 can be written as (x+2) (x^2-2x+4)

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anonymous
  • anonymous
Thank you sooo much. Can I bother you with one more problem?
anonymous
  • anonymous
It's not a bother.
anonymous
  • anonymous
\[\lim_{n \rightarrow 0} \sin 3x/ \sin2x\]
anonymous
  • 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
anonymous
  • anonymous
For the denominator i mean
anonymous
  • anonymous
Xavier, I'm still trying to figure out how you changed x^3+8 to (x+2) (x^2-2x+4)
anonymous
  • anonymous
I prayed that (x+2) is a factor and divided.
anonymous
  • anonymous
Oh, prayer answered.

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