anonymous
  • anonymous
limit as x approaches 3 of ((x^2)-x-6)/(1-(sqrt(10-3*x)))
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I multiplied denominator by 1+sqrt(10-3) to cancel square root and factored out a -3 to get (-3(x+3)) then factoring the top i get (x+2)(x-3) though do not see any cancelation from here due to the fact that I still need to multiply by 1+sqrt(10-3)
BAdhi
  • BAdhi
after multiplying the denominator you should get \(1-\sqrt{10-3x}^2=1-(10-3x)\) which is equal to \(3(x-3)\) the (x-3) in this should cancel out with (x-3) on the numerator. Now you should be able to find the limit
anonymous
  • anonymous
which is essentially what I was trying to do, though (possibly i am not seeing it) this does not equal 3(x-3) because 1-10-3x =-9-3x = 3(-x-3)

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BAdhi
  • BAdhi
\[\begin{align*} (1-\sqrt{10-3x})(1+\sqrt{10-3x})&=1^2-[\sqrt{10-3x}]^2\\ &=1-(10-3x)\\ &=1-10\textbf{+}3x\\ &=3x-9\\ &=3(x-3) \end{align*}\] alfterall, you should know that the denominator should have a factor (x-3) because when substituted x=3, you get 0 for the denominator \(1-\sqrt{10-3x}\) (which is the reason to consider algebraic alteration of the expression from the first place)
anonymous
  • anonymous
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BAdhi
  • BAdhi
yes well done :). But, make sure that you don't use \(\lim \limits_{x \to 3}\), after substituting the value
anonymous
  • anonymous
very well...thank you for putting me in check on my 3rd grade algebra skills!
BAdhi
  • BAdhi
It's a pleasure :).

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