$lim_(x->oo)(x-1)/(2x+cos(x))=$ ?

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Answer 1 · 2016-12-09T10:59:16

$1/2$

$(x-1)/(2x+cos(x))=x/x(1-1/x)/(2+cos(x)/x) = (1-1/x)/(2+cos(x)/x)$

$lim_(x->oo)(x-1)/(2x+cos(x))=(lim_(x->oo)(1-1/x))/(lim_(x->oo)(2+cos(x)/x)) = 1/2$

Note that $abs(cos(x)) le 1$

lim_(x->oo)(x-1)/(2x+cos(x))=lim_(x->oo)(x-1)/(2x+cos(x))= ?