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Mathematics 15 Online
OpenStudy (anonymous):

Find the limit of f(x) as x approaches infinity: f(x)=cos(1/x)/(1+(1/x)) if you can help please explain each step.

OpenStudy (anonymous):

i think you get 1 by inspection

OpenStudy (anonymous):

meaning \[\lim_{x\rightarrow \infty}\frac{1}{x}=0\] as since cosine is continuous this means \[\lim_{x\rightarrow \infty}\cos(\frac{1}{x})=\cos(0)=1\]

OpenStudy (anonymous):

likewise \[\lim_{x\rightarrow \infty}(1+\frac{1}{x})=1+0=1\]so the whole thing is \[\frac{1}{1}=1\]

OpenStudy (anonymous):

think all the steps are there. "by inspection" meant no tricks or l'hopital's rule

OpenStudy (anonymous):

so you found the limit of the numerator and the limit of the denominator and made that the answer? you can do that?

OpenStudy (anonymous):

yes

OpenStudy (anonymous):

you can do it unless you get \[\frac{0}{0}\] then you have to do more work

OpenStudy (anonymous):

right. teacher emphasized sandwich theorem in lecture so i've attempted to find it that way with no luck. do you know how to do it that way?

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