Calculate limit (x^2+2x+1)/(2x^2-2x-1), x->+infinity

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limit (x^2+2x+1)/(2x^2-2x-1)  when x--> inf

We observe that he highest power for the numerator and denominator is x^2, then we divide both functions by x^2.

==> lim x^2(1+2/x+1/x^2)/lim x^2(2-2/x-1/x^2)

==> lim (1+2/x+1/x^2)/lim (2-2/x-1/x^2) = (1+0+0)/(2-0-0)=1/2

then the limit when x--> inf is 1/2

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limit (x^2+2x+1)/(2x^2-2x-1)  when x--> inf

We observe that he highest power for the numerator and denominator is x^2, then we divide both functions by x^2.

==> lim x^2(1+2/x+1/x^2)/lim x^2(2-2/x-1/x^2)

==> lim (1+2/x+1/x^2)/lim (2-2/x-1/x^2) = (1+0+0)/(2-0-0)=1/2

then the limit when x--> inf is 1/2

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