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lim-x-cos-2-x-x-1-2x-




Question Number 66434 by iklima_0412 last updated on 15/Aug/19
lim_(x→∞)  ((cos^2 x−x)/(1−2x))
limxcos2xx12x
Commented by mathmax by abdo last updated on 15/Aug/19
let f(x)=((cos^2 x−x)/(1−2x)) ⇒ for x ≠0  we have f(x)=((x−cos^2 x)/(2x−1))  =((x(1−((cos^2 x)/x)))/(x(2−(1/x)))) =((1−((cos^2 x)/x))/(2−(1/x)))  but lim_(x→+∞)    ((cos^2 x)/x) =0 becsuse ∣cosx∣≤1  lim_(x→+∞)  (1/x) =0 ⇒lim_(x→+∞) f(x)=(1/2)
letf(x)=cos2xx12xforx0wehavef(x)=xcos2x2x1=x(1cos2xx)x(21x)=1cos2xx21xbutlimx+cos2xx=0becsusecosx∣⩽1limx+1x=0limx+f(x)=12
Commented by kaivan.ahmadi last updated on 15/Aug/19
≡lim_(x→∞)  ((−x)/(−2x))=(1/2)
limxx2x=12

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