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ConDawg

  • 3 years ago

Evaluate the following limit. If the answer is positive infinite, type "I"; if negative infinite, type "N"; and if it does not exist, type "D". lim ---> 4/9x+3 x goes to infinity

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  1. Callisto
    • 3 years ago
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    Is it \[\lim_{x \rightarrow \infty} \frac{4}{9x+3}\] for your question?

  2. ConDawg
    • 3 years ago
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    yes sorry!! I was busy doing other practice questions for my test tomorrow.

  3. Callisto
    • 3 years ago
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    Never mind :) 1. Divide both numerator and denominator by x, what do you get?

  4. ConDawg
    • 3 years ago
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    |dw:1350532389029:dw|

  5. Callisto
    • 3 years ago
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    Yup! Now, you need to know that \[\lim_{x \rightarrow \infty}\frac{1}{x} = 0\]Now, can you evaluate the limit?

  6. ConDawg
    • 3 years ago
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    what does the 1/x = 0 mean? does that also mean that 4/x - 0?

  7. ConDawg
    • 3 years ago
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    4/x=0

  8. Callisto
    • 3 years ago
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    It's \[\lim_{x \rightarrow \infty \frac{1}{x}} = 0\] Imagine 1 is divided by a very large number, then you probably get 0.

  9. Callisto
    • 3 years ago
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    Aww.. Bad typing! It's \[\lim_{x \rightarrow \infty} \frac{1}{x}=0\]

  10. ConDawg
    • 3 years ago
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    so 4 divide by a very large number is pretty much 0, so I think the answer should be 0/9.

  11. Callisto
    • 3 years ago
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    Yup! Which is...?

  12. ConDawg
    • 3 years ago
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    0

  13. Callisto
    • 3 years ago
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    You got it!

  14. ConDawg
    • 3 years ago
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    :) Thank you! It's greatly appreciated!

  15. Callisto
    • 3 years ago
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    Just a little summary of the above: \[\lim_{x \rightarrow \infty} \frac{4}{9x+3}\]Divide both numerator and denominator by x\[\lim_{x \rightarrow \infty} \frac{\frac{4}{x}}{\frac{9x+3}{x}}\]\[=\lim_{x \rightarrow \infty} \frac{\frac{4}{x}}{9+\frac{3}{x}}\]\[= \frac{\lim_{x \rightarrow \infty}(\frac{4}{x})}{\lim_{x \rightarrow \infty}(9)+\lim_{x \rightarrow \infty}(\frac{3}{x})}\]And then evaluate the limit by using \[\lim_{x \rightarrow \infty}\frac{1}{x} = 0\]

  16. ConDawg
    • 3 years ago
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    One question, how did you know to divide by x at the first?

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