anonymous
  • anonymous
can someone explain how to find the limit x-->3 using (9-x^2)/(x-3)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Think you have this : 7x = 70 How do you answer ?!:)
anonymous
  • anonymous
x=10
anonymous
  • anonymous
Excelent ! Now when we want to find x in your problem can use this way but do you want to know a better way ?!:) :D

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anonymous
  • anonymous
wait if i solve for x is that going to give me the limit as x approaches 3?
anonymous
  • anonymous
Exacly friend !:) :D
anonymous
  • anonymous
okay thank you!
amistre64
  • amistre64
that might be a little misleading ... the limit of a function does not care what the value of the function is
amistre64
  • amistre64
since at x=3, we get 0/0 the value is undetermined. the limit is defined to be the value that the function approaches, from the left and right. regardless of the actual value of the function
amistre64
  • amistre64
in this case, we can algebra the top to provide an equivalent setup that cancels out the bottom; so that we do not possess a divide by zero result
amistre64
  • amistre64
what does the top factor out to be? consider that (x-3) is a factor.
phi
  • phi
as amistre said, a good step is factor the top in \[ \frac{(9-x^2)}{(x-3)} \] notice the top is a "difference of squares", a^2 - b^2 which factors into (a+b)(a-b) if you factor you get \[ \frac{(3+x)(3-x))}{(x-3)} \] notice that you can cancel (x-3) from the top and bottom (as long as x is not *exactly* 3) you get 3+x now let x -->3 what value are you approaching ?
anonymous
  • anonymous
-6! Sweet thanks so much you guys!!!!
phi
  • phi
I hope you are not saying 3+3 = -6 don't you mean +6 ?

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