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anonymous

  • 4 years ago

another...lim x->0, x+xcosx/sinxcosx?

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  1. anonymous
    • 4 years ago
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    factor

  2. anonymous
    • 4 years ago
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    \[\frac{x(1+\cos(x))}{\sin(x)\cos(x)}\] the break in two parts as before

  3. anonymous
    • 4 years ago
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    i got that far...let me c if the next step jumps out at me

  4. anonymous
    • 4 years ago
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    think about a limit that you know (hint, sine) and a limit that is obvious

  5. anonymous
    • 4 years ago
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    haha its not

  6. anonymous
    • 4 years ago
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    k...

  7. anonymous
    • 4 years ago
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    limit is 0, but its not clicking...

  8. anonymous
    • 4 years ago
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    that is because it is not zero

  9. anonymous
    • 4 years ago
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    oh man that i am really lost now..i thought the lim of sine at 0 is 0?

  10. anonymous
    • 4 years ago
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    \[\frac{x}{\sin(x)}\times \frac{1+\cos(x)}{cos(x)}\]

  11. anonymous
    • 4 years ago
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    x/sinx=1 righ?

  12. Zarkon
    • 4 years ago
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    as x goes to zero...yes

  13. anonymous
    • 4 years ago
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    still lost on how the 2 comes out as the answer?

  14. anonymous
    • 4 years ago
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    does 1+cosx/cosx=2?

  15. Zarkon
    • 4 years ago
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    cos(0)=1

  16. Zarkon
    • 4 years ago
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    (1+1)/1=2

  17. anonymous
    • 4 years ago
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    1+cos(x) is 1+1?

  18. anonymous
    • 4 years ago
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    got it!!!!!!!

  19. Zarkon
    • 4 years ago
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    \[\lim_{x\to 0}\frac{1+\cos(x)}{\cos(x)}=\frac{1+1}{1}=2\]

  20. anonymous
    • 4 years ago
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    thanks zarkon and satel!!!

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spraguer (Moderator)
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