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adam32885

  • 2 years ago

limit help

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  1. perl
    • 2 years ago
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    whats the question>

  2. adam32885
    • 2 years ago
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    \[\lim_{x \rightarrow 1}\frac{ x-1 }{ \sqrt[3]{x+7}-2 }\]

  3. adam32885
    • 2 years ago
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    I am having trouble with this equation we are given the hint make the substation x+7=t^3

  4. Azteck
    • 2 years ago
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    Rationalise the denominator by multiplying by \[\frac{ \sqrt[3]{(x+7)^2}+2 }{ \sqrt[3]{(x+7)^2}+2 } \]

  5. Azteck
    • 2 years ago
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    Oh now you say you were given that.

  6. Azteck
    • 2 years ago
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    \[=\frac{ t^3-7-1 }{ t-2 }\]

  7. Yahoo!
    • 2 years ago
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    x+7=t^3 as x ---> 1 t ----> 2

  8. Azteck
    • 2 years ago
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    Factorise

  9. Azteck
    • 2 years ago
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    And you can get rid of the denominator. Once you do that. Sub back the x's.

  10. adam32885
    • 2 years ago
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    so when i make the sub I get \[\lim_{x \rightarrow 1} \frac{ x-1 }{ t+2 }\] ?

  11. Azteck
    • 2 years ago
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    No you sub the x on the numerator as well.

  12. Yahoo!
    • 2 years ago
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    a^3 - b^3 = (a-b) (a^2 +ab + b^2

  13. Azteck
    • 2 years ago
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    \[t^3=x+7\] make x the subject. \[x=t^3-7\]

  14. Azteck
    • 2 years ago
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    Now sub the x on the numerator with t^3-7

  15. adam32885
    • 2 years ago
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    oh now i get it. pass the duh stamp

  16. Azteck
    • 2 years ago
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    Now you can get rid of that denominator.

  17. Azteck
    • 2 years ago
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    Once you do that, remember to replace the t's with \[\sqrt[3]{x+7}\]

  18. Azteck
    • 2 years ago
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    and then you can then sub in x=1 to find the limit.

  19. adam32885
    • 2 years ago
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    got it thank you!

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