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.

i think you get 1 by inspection

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

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

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

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

yes

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

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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