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calculus130

  • 2 years ago

step by step using L'hopital rule: limit of 1+cos(x)/x * sin(x) as x approaches π

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  1. nubeer
    • 2 years ago
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    put pi in place of x. and see what you got.

  2. nubeer
    • 2 years ago
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    hint cos pi = -1 sin pi = 0

  3. calculus130
    • 2 years ago
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    i get 0/0 if i plug pi with x

  4. nubeer
    • 2 years ago
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    yes.. now apply the derivative in numerator and seperately in denominator.

  5. calculus130
    • 2 years ago
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    i get -sinx/-xcosx

  6. calculus130
    • 2 years ago
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    after plugging the ans is 0/-1

  7. nubeer
    • 2 years ago
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    hmm please check the derivative in denominator again.. i think its wrong.. look you have to x in there so i believe you have to find derivative with product rule.

  8. richyw
    • 2 years ago
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    to compute\(\frac{d}{dx}\left(x\sin x\right)\) you need to use the product rule.

  9. richyw
    • 2 years ago
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    \[=x\cos x+\sin x\]

  10. richyw
    • 2 years ago
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    \[=\lim_{x\rightarrow \pi}\frac{-\cos x}{\sin x +x\cos x}\]\[=\frac{0}{1+\pi\cdot 0}\]\[=0\]

  11. calculus130
    • 2 years ago
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    thnx

  12. nubeer
    • 2 years ago
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    i believe cos pi = -1 so how come got 0 in numerator.

  13. richyw
    • 2 years ago
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    wow. big mistake haha

  14. nubeer
    • 2 years ago
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    lol no worries.. :P happens sometimes with me too :P

  15. richyw
    • 2 years ago
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    or wait, sorry I meant I had the wrong numerator the numberator should be sine

  16. richyw
    • 2 years ago
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    \[\lim_{x\rightarrow \pi}\frac{-\sin x}{\sin x +x\cos x}\]Still works out to 0/1=0

  17. richyw
    • 2 years ago
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    or actuall \(0/-\pi\)=0 haha.

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