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dgamma3

How would you solve the following limit: limit (x -> 0+) (x-11)/sin(x)

  • one year ago
  • one year ago

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  1. dgamma3
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    you can do it manually, and figure out its negative infinity. but is there any algebraic way.

    • one year ago
  2. dgamma3
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    \[\lim_{x \rightarrow 0+} (x-11)/\sin(x)\]

    • one year ago
  3. nitz
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    \[\lim_{x \rightarrow 0}(sinx/x)=1\]

    • one year ago
  4. kirbykirby
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    \[You know \lim_{x \rightarrow 0+} \frac{\sin x}{x}=1 \]

    • one year ago
  5. kirbykirby
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    so: do the same trick I told you before: Divide the top and bottom by x

    • one year ago
  6. nitz
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    and \[\lim_{x \rightarrow 0}(11/sinx)\rightarrow \infty \]

    • one year ago
  7. kirbykirby
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    \[\lim_{x \rightarrow 0+} \frac{\frac{11-x}{x}}{\frac{\sin x}{x}} = \lim_{x \rightarrow 0+} \frac{11/x-1}{\frac{\sin x}{x}}=\]\[\frac{\infty-1}{1}=\infty\]

    • one year ago
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