anonymous
  • anonymous
Limits, Cal 1 lim √(x+19) -4 / (x²+3x) x-->3 My teacher wants us to TRY these but she is out of town so she cannot answer our questions, our library is under construction and that is where the tutoring takes place so they are not available and my book has not come in. No one can seem to help me with this problem. Can anyone show a step by step solution? I am stumped :/ Idk how to start at all.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
And that is supposed to be "x--> -3" not "x-->3"
anonymous
  • anonymous
Using L'Hopital's rule, lim(x-->-3) of f(x)/g(x) = lim(x-->-3) of ((d/dx)f(x)/(d/dx)g(x)). When I do this I get 1/[2*((x+19)^(1/2))*(2x+3)]. Taking the limit of this as x goes to -3, I get -(1/24).
anonymous
  • anonymous
do you know l'hopital, or are you supposed to use something else?

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anonymous
  • anonymous
your best bet is to factor the denominator, then multiply top and bottom by \(\sqrt{x+19}+4\)
anonymous
  • anonymous
then numerator will be \(x+3\) which will cancel with the factor of \(x+3\) in the denominator then you can plug in the \(-3\) to get your answer
anonymous
  • anonymous
so you're saying it will look like this: \[\frac{ x+3 }{x+3 } \] and then plug in "-3" for x?

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