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roseflight

  • 3 years ago

What is the limit of sin(2x)/(3x) as x approaches 0

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  1. zordoloom
    • 3 years ago
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    Would you like the step by step?

  2. roseflight
    • 3 years ago
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    Yes please

  3. TuringTest
    • 3 years ago
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    \[\frac{\sin(2x)}{3x}=\frac13\cdot\frac{\sin(2x)}x=\frac23\cdot\frac{\sin(2x)}{2x}\]

  4. roseflight
    • 3 years ago
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    Sorry, but I still don't get how that would equal 2/3.

  5. TuringTest
    • 3 years ago
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    did you know that\[\lim_{x\to0}\frac{\sin x}x=1\]?

  6. roseflight
    • 3 years ago
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    Haha I didn't remember that for some reason. Thanks!

  7. dpaInc
    • 3 years ago
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    how 'bout this then.... \(\large \frac{sin(2x)}{3x}=\frac{2sinxcosx}{3x}=\frac{2}{3}\cdot \frac{sinx}{x}\cdot cosx \)

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