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Study23

  • 2 years ago

Limits help (kind of forgot...) Click here to see function

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  1. Study23
    • 2 years ago
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    \[ \huge \lim_{x \rightarrow 2} \frac{(x-3)(x+2)}{(x-2)}.\]

  2. Study23
    • 2 years ago
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    How can I simplify the denominator so that it doesnt give me a 0..?

  3. satellite73
    • 2 years ago
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    numerator is not zero, so go fish

  4. hartnn
    • 2 years ago
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    directly put x=2

  5. satellite73
    • 2 years ago
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    i.e. no limit

  6. Study23
    • 2 years ago
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    ? Wouldn't it be a a denominator of 0, which is a "no-no"?

  7. satellite73
    • 2 years ago
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    if you get a zero in the denominator, but not a zero in the numerator, then there is no limit only when you get \(\frac{0}{0}\) can you continue if you get a zero in the denominator

  8. satellite73
    • 2 years ago
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    no

  9. Study23
    • 2 years ago
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    No, We haven't learned about that yet

  10. satellite73
    • 2 years ago
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    l'hopital works for \(\frac{0}{0}\) in any case you didn't get there yet i am sure

  11. Study23
    • 2 years ago
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    So, @satellite73 would the limit be DNE ?

  12. Study23
    • 2 years ago
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    Because my teacher always says to only substitute directly when the denominator is not equal to zero...

  13. satellite73
    • 2 years ago
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    not applicable here if you have a rational funciton, and you want to take the limit as x goes to some number, the first step is to plug in the number if you get a number back, that is your answer if you get \(\frac{a}{0}\) where \(a\neq 0\) there is no limit if you get \(\frac{0}{0}\) there is more work to be done factor and cancel but in this case you get \(\frac{-4}{0}\) so forget it

  14. Study23
    • 2 years ago
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    That makes a lot of sense @satellite73! Thanks so much!!

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