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

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

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

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

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

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

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

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

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

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

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

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