16.
\(q=\dfrac{u_2}{u_1}=\dfrac{1}{3}\)
1.
\(A=\lim\limits_{x\rightarrow-\infty}\dfrac{3-x}{x+2}=\lim\limits_{x\rightarrow-\infty}\dfrac{x\left(\dfrac{3}{x}-1\right)}{x\left(1+\dfrac{2}{x}\right)}=\lim\limits_{x\rightarrow-\infty}\dfrac{\dfrac{3}{x}-1}{1+\dfrac{2}{x}}=\dfrac{0-1}{1+0}=-1\)
2.
\(B=\lim\limits_{x\rightarrow1}\dfrac{2x-\sqrt{x+3}}{x^2-1}=\lim\limits_{x\rightarrow1}\dfrac{\left(2x-\sqrt{x+3}\right)\left(2x+\sqrt{x+3}\right)}{\left(x-1\right)\left(x+1\right)\left(2x+\sqrt{x+3}\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{4x^2-x-3}{\left(x-1\right)\left(x+1\right)\left(2x+\sqrt{x+3}\right)}=\lim\limits_{x\rightarrow1}\dfrac{\left(x-1\right)\left(4x+3\right)}{\left(x-1\right)\left(x+1\right)\left(2x+\sqrt{x+3}\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{4x+3}{\left(x+1\right)\left(2x+\sqrt{x+3}\right)}=\dfrac{4.1+3}{\left(1+1\right)\left(2.1+\sqrt{1+3}\right)}=\dfrac{7}{8}\)
