Câu 1.
\(lim\left(\sqrt{n^2+2n+5}-\sqrt{n^2+n}\right)\)
Nhân liên hợp ta đc:
\(lim\left(\dfrac{n^2+2n+5-\left(n^2+n\right)}{\sqrt{n^2+2n+5}+\sqrt{n^2+n}}\right)\)
\(=lim\left(\dfrac{n+5}{n\sqrt{1+\dfrac{2}{n}+\dfrac{5}{n^2}}+n\sqrt{1+\dfrac{1}{n}}}\right)\)
\(=lim\left(\dfrac{n+\dfrac{5}{n}}{n\sqrt{1}+n\sqrt{1}}\right)=lim\left(\dfrac{n}{2n}\right)=lim\dfrac{1}{2}=\dfrac{1}{2}\)
Chọn C
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