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calculus130
 3 years ago
step by step using L'hopital rule:
limit of 1+cos(x)/x * sin(x) as x approaches π
calculus130
 3 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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nubeer
 3 years ago
Best ResponseYou've already chosen the best response.0put pi in place of x. and see what you got.

nubeer
 3 years ago
Best ResponseYou've already chosen the best response.0hint cos pi = 1 sin pi = 0

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

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

calculus130
 3 years ago
Best ResponseYou've already chosen the best response.0after plugging the ans is 0/1

nubeer
 3 years ago
Best ResponseYou've already chosen the best response.0hmm 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
 3 years ago
Best ResponseYou've already chosen the best response.0to compute\(\frac{d}{dx}\left(x\sin x\right)\) you need to use the product rule.

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

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

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

richyw
 3 years ago
Best ResponseYou've already chosen the best response.0or wait, sorry I meant I had the wrong numerator the numberator should be sine

richyw
 3 years ago
Best 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

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