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anonymous

  • 5 years ago

Compute lim x->0 (4x/sin(3x)+x/cos(3x))

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  1. myininaya
    • 5 years ago
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    \[\lim_{x \rightarrow 0}(\frac{4x}{\sin(3x)}+\frac{x}{\cos(3x)}=\frac{4}{3}\lim_{x \rightarrow 0}\frac{3x}{\sin(3x)}+\lim_{x \rightarrow 0}\frac{x}{\cos(3x)}\] Recall \[\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1\]

  2. myininaya
    • 5 years ago
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    the other one is just direct sub.

  3. anonymous
    • 5 years ago
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    i didnt quite understand what you just showed =/

  4. myininaya
    • 5 years ago
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    Nothing?

  5. anonymous
    • 5 years ago
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    okay so what did you do their when you put 4/3

  6. myininaya
    • 5 years ago
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    4/3 * 3 =4 I just multiplied the first fraction by 3/3

  7. anonymous
    • 5 years ago
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    which became 12x/sin(9x)?

  8. myininaya
    • 5 years ago
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    oh no

  9. myininaya
    • 5 years ago
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    3sin(3x) does not equal sin(9x)

  10. anonymous
    • 5 years ago
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    oh ur right lol sorry about that

  11. anonymous
    • 5 years ago
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    whats the purpose of multiplying by 3/3?

  12. myininaya
    • 5 years ago
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    \[\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1\] Do you recall this?

  13. anonymous
    • 5 years ago
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    i dont

  14. myininaya
    • 5 years ago
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    so this means we can say \[\lim_{x \rightarrow 0}\frac{3x}{\sin(3x)}=1\]

  15. anonymous
    • 5 years ago
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    alright

  16. myininaya
    • 5 years ago
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    so I wanted a 3 up there in our problem

  17. myininaya
    • 5 years ago
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    but if i put a 3 on top I have to put a 3 on bottom

  18. anonymous
    • 5 years ago
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    yes

  19. myininaya
    • 5 years ago
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    so that is why I multiplied by 3/3

  20. anonymous
    • 5 years ago
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    i get it so the first part became 1

  21. myininaya
    • 5 years ago
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    yes 4/3 times 1 is the first part

  22. myininaya
    • 5 years ago
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    not the second part we just plug in 0

  23. myininaya
    • 5 years ago
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    now*

  24. myininaya
    • 5 years ago
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    is everything ok? you got it?

  25. anonymous
    • 5 years ago
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    im writing it down

  26. myininaya
    • 5 years ago
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    ok

  27. anonymous
    • 5 years ago
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    so then it would be 0/cos(3(0))

  28. myininaya
    • 5 years ago
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    0/1=0

  29. myininaya
    • 5 years ago
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    yes

  30. myininaya
    • 5 years ago
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    so we have 4/3 from the first part+ 0 from the second part =4/3

  31. anonymous
    • 5 years ago
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    oh got it thanks!

  32. myininaya
    • 5 years ago
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    :)

  33. myininaya
    • 5 years ago
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    Spikey I appreciate that you want to learn this stuff. Thanks for engaging in the learning process. That is really cool dude.

  34. anonymous
    • 5 years ago
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    lol thank you :) i take AP calc

  35. anonymous
    • 5 years ago
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    in highschool

  36. myininaya
    • 5 years ago
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    Go you! :)

  37. myininaya
    • 5 years ago
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    It is really cool to have that attitude. You will go far.

  38. anonymous
    • 5 years ago
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    theres just some stuff that i dont really comprehend my teacher doesnt teach some stuff clearly

  39. anonymous
    • 5 years ago
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    lol yeah i never give up. :)

  40. anonymous
    • 5 years ago
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    always trying to learn new things.

  41. myininaya
    • 5 years ago
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    Good luck to you and peace out!

  42. anonymous
    • 5 years ago
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    lol bye

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