Question

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

Answer 1

put pi in place of x. and see what you got.

Answer 2

hint
cos pi = -1
sin pi = 0

Answer 3

i get 0/0 if i plug pi with x

Answer 4

yes.. now apply the derivative in numerator and seperately in denominator.

Answer 5

i get -sinx/-xcosx

Answer 6

after plugging the ans is 0/-1

Answer 7

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.

Answer 8

to compute\(\frac{d}{dx}\left(x\sin x\right)\) you need to use the product rule.

Answer 9

\[=x\cos x+\sin x\]

Answer 10

\[=\lim_{x\rightarrow \pi}\frac{-\cos x}{\sin x +x\cos x}\]\[=\frac{0}{1+\pi\cdot 0}\]\[=0\]

Answer 11

thnx

Answer 12

i believe cos pi = -1
so how come got 0 in numerator.

Answer 13

wow. big mistake haha

Answer 14

lol no worries.. :P happens sometimes with me too :P

Answer 15

or wait, sorry I meant I had the wrong numerator the numberator should be sine

Answer 16

\[\lim_{x\rightarrow \pi}\frac{-\sin x}{\sin x +x\cos x}\]Still works out to 0/1=0

Answer 17

or actuall \(0/-\pi\)=0 haha.