anonymous
  • anonymous
step by step using L'hopital rule: limit of 1+cos(x)/x * sin(x) as x approaches π
Mathematics
chestercat
  • chestercat
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nubeer
  • nubeer
put pi in place of x. and see what you got.
nubeer
  • nubeer
hint cos pi = -1 sin pi = 0
anonymous
  • anonymous
i get 0/0 if i plug pi with x

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nubeer
  • nubeer
yes.. now apply the derivative in numerator and seperately in denominator.
anonymous
  • anonymous
i get -sinx/-xcosx
anonymous
  • anonymous
after plugging the ans is 0/-1
nubeer
  • nubeer
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.
richyw
  • richyw
to compute\(\frac{d}{dx}\left(x\sin x\right)\) you need to use the product rule.
richyw
  • richyw
\[=x\cos x+\sin x\]
richyw
  • richyw
\[=\lim_{x\rightarrow \pi}\frac{-\cos x}{\sin x +x\cos x}\]\[=\frac{0}{1+\pi\cdot 0}\]\[=0\]
anonymous
  • anonymous
thnx
nubeer
  • nubeer
i believe cos pi = -1 so how come got 0 in numerator.
richyw
  • richyw
wow. big mistake haha
nubeer
  • nubeer
lol no worries.. :P happens sometimes with me too :P
richyw
  • richyw
or wait, sorry I meant I had the wrong numerator the numberator should be sine
richyw
  • richyw
\[\lim_{x\rightarrow \pi}\frac{-\sin x}{\sin x +x\cos x}\]Still works out to 0/1=0
richyw
  • richyw
or actuall \(0/-\pi\)=0 haha.

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