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calculus130
Group Title
step by step using L'hopital rule:
limit of 1+cos(x)/x * sin(x) as x approaches π
 one year ago
 one year ago
calculus130 Group Title
step by step using L'hopital rule: limit of 1+cos(x)/x * sin(x) as x approaches π
 one year ago
 one year ago

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nubeer Group TitleBest ResponseYou've already chosen the best response.0
put pi in place of x. and see what you got.
 one year ago

nubeer Group TitleBest ResponseYou've already chosen the best response.0
hint cos pi = 1 sin pi = 0
 one year ago

calculus130 Group TitleBest ResponseYou've already chosen the best response.0
i get 0/0 if i plug pi with x
 one year ago

nubeer Group TitleBest ResponseYou've already chosen the best response.0
yes.. now apply the derivative in numerator and seperately in denominator.
 one year ago

calculus130 Group TitleBest ResponseYou've already chosen the best response.0
i get sinx/xcosx
 one year ago

calculus130 Group TitleBest ResponseYou've already chosen the best response.0
after plugging the ans is 0/1
 one year ago

nubeer Group TitleBest ResponseYou've already chosen the best response.0
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.
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
to compute\(\frac{d}{dx}\left(x\sin x\right)\) you need to use the product rule.
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
\[=x\cos x+\sin x\]
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
\[=\lim_{x\rightarrow \pi}\frac{\cos x}{\sin x +x\cos x}\]\[=\frac{0}{1+\pi\cdot 0}\]\[=0\]
 one year ago

nubeer Group TitleBest ResponseYou've already chosen the best response.0
i believe cos pi = 1 so how come got 0 in numerator.
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
wow. big mistake haha
 one year ago

nubeer Group TitleBest ResponseYou've already chosen the best response.0
lol no worries.. :P happens sometimes with me too :P
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
or wait, sorry I meant I had the wrong numerator the numberator should be sine
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
\[\lim_{x\rightarrow \pi}\frac{\sin x}{\sin x +x\cos x}\]Still works out to 0/1=0
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
or actuall \(0/\pi\)=0 haha.
 one year ago
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