Question

Answer 1

36.

a, \(lim\left(\sqrt{n^2+n+1}-n\right)\)

\(=lim\dfrac{n^2+n+1-n^2}{\sqrt{n^2+n+1}+n}\)

\(=lim\dfrac{n+1}{\sqrt{n^2+n+1}+n}\)

\(=lim\dfrac{1+\dfrac{1}{n}}{\sqrt{1+\dfrac{1}{n}+\dfrac{1}{n^2}}+1}\)

\(=\dfrac{1}{2}\)

Answer 2

36.

b, \(\lim\limits_{x\rightarrow-\infty}\dfrac{x^2+2x-3}{2x^2-5x}\)

\(=\lim\limits_{x\rightarrow-\infty}\dfrac{1+\dfrac{2}{x}-\dfrac{3}{x^2}}{2-\dfrac{5}{x}}\)

\(=\dfrac{1}{2}\)