calculus question find the points of discontinuity, and determine whether the discontinuties are removable
f(x)=x^2-4/x^3-8

Question

calculus question find the points of discontinuity, and determine whether the discontinuties are removable 
f(x)=x^2-4/x^3-8

anonymous · Answer

factor factor factor
then cancel

anonymous · Answer

how do you factor the bottom

anonymous · Answer

do you know how to factor 
$$x^3-8$$?

anonymous · Answer

you are going to need this one in calc, so best to memorize it 
$$a^3-b^3=(a-b)(a^2+ab+b^2)$$

anonymous · Answer

in your case $a=x,b=2$

anonymous · Answer

thank you!

anonymous · Answer

once you cancel, you have "removed" the discontinuity, so it will be "removable"

anonymous · Answer

so the removable disconuity would be 2

anonymous · Answer

yes

anonymous · Answer

ok thank you

anonymous · Answer

denominator is 0 at $x=2$ so it is the function is discontinuous there
but since if $x\neq 2$ this whole thing is 
$$\frac{x+2}{x^2+2x+4}$$ and since the denominator is never zero, you have only one discontinuity at $x=2$ and you have just removed it

anonymous · Answer

yw