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anonymous

  • one year ago

Find the limit of the function using cancellation techniques (-6 + x) / x^4 Please explain.

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  1. anonymous
    • one year ago
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    I know how to do cancellation, but only with numerators that are factor-able.

  2. anonymous
    • one year ago
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    Like Use cancellation techniques to evaluate limit as x approaches -1 of 2x squared minus x minus 3 divided by (x + 1). You can factor the numerator as (2x -3)(x + 1). After cancelling out the common factor of (x+1), the limit can be evaluated using direct substation. The limit is equal to -5

  3. Luigi0210
    • one year ago
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    @hartnn can help ya (:

  4. hartnn
    • one year ago
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    separate the numerator \(-6/x^4 \) + \(x/x^4\) cancel out one x in the 2nd term

  5. anonymous
    • one year ago
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    So \[-6/x^4 + x^3\]

  6. hartnn
    • one year ago
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    -6/x^4 + 1/x^3

  7. anonymous
    • one year ago
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    Why is 1 in the numerator?

  8. hartnn
    • one year ago
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    |dw:1436550810803:dw|

  9. anonymous
    • one year ago
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    Oh, that went right over my head.

  10. anonymous
    • one year ago
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    So wouldn't it be 0 as the limit?

  11. hartnn
    • one year ago
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    where does the x approach? x-> 0 ?

  12. anonymous
    • one year ago
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    I don't know. I was taught to just to insert whatever number, in this case 0, in the factored equation.

  13. hartnn
    • one year ago
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    "in this case 0" you deduced that from the question, right?

  14. anonymous
    • one year ago
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    Yeah. Wait, wouldn't it not exist?

  15. hartnn
    • one year ago
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    " just to insert whatever number" is the worst way anyone can teach limits :P

  16. anonymous
    • one year ago
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    It's virtual school. .-.

  17. hartnn
    • one year ago
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    if x approaches 0, the numerator is negative, the denominator is very very near to 0 hence the limit will approach -infinity :)

  18. anonymous
    • one year ago
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    Thats not an option...

  19. hartnn
    • one year ago
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    *** negative number /0 = -infinity

  20. hartnn
    • one year ago
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    what are the options? can yo post the screenshot of entire question and options?

  21. anonymous
    • one year ago
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  22. hartnn
    • one year ago
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    so they haven't introduced you to infinity yet... in that case, you can choose "Does Not Exist" as the answer. even though the limit exist and = - infinity

  23. anonymous
    • one year ago
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    Exactly! It's basic math, but some websites say it would be 0, if and only if the x--> infinity.

  24. hartnn
    • one year ago
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    when x-> infinity, means x is a very large number then 1/x will be very small number hence, 1/x^3 and 1/x^4 will approach 0 hence you limit will be = 0

  25. anonymous
    • one year ago
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    Yep. Thank you for the help! I really appreciated it. cx

  26. hartnn
    • one year ago
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    welcome ^_^

  27. anonymous
    • one year ago
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    It was that they did not exist. cx @hartnn

  28. hartnn
    • one year ago
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    so we were correct :)

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