$1.1\quad A =\lim\dfrac{6n^3 - 2n +3}{2n^3 - 3n^2 - 5n +1}$
$\to A =\lim\dfrac{6 -\dfrac{2}{n^2} +\dfrac{3}{n^3}}{2-\dfrac3n -\dfrac{5}{n^2} +\dfrac{1}{n^3}}$
$\to A =\dfrac{6 - 0+ 0}{2 -0-0+0}$
$\to A = \dfrac62 = 3$
$2.1 \quad A =\lim\dfrac{4n^5 - 3n^4 - 2n^3 + 7n -9}{-5n(3n^2 - 2n+1)(5-2n^2)}$
$\to A =\lim\dfrac{4 - \dfrac3n -\dfrac{2}{n^2} +\dfrac{7}{n^4} -\dfrac{9}{n^5}}{-5\left(3 -\dfrac2n +\dfrac{1}{n^2}\right)\left(\dfrac{5}{n^2} -2\right)}$
$\to A =\dfrac{4 -0-0+0-0}{-5(3-0+0)(0-2)}$
$\to A =\dfrac{4}{-5.3.(-2)}$
$\to A =\dfrac{2}{15}$
$2.3\quad C =\lim\dfrac{(2n+1)(n-3) + 3n^2}{-3n^3 + 2n +7}$
$\to C =\lim\dfrac{\dfrac1n\cdot\left(2+\dfrac1n\right)\left(1-\dfrac3n\right) +\dfrac3n}{-3 +\dfrac{2}{n^2} +\dfrac{7}{n^3}}$
$\to C =\dfrac{0.(2+0)(1-0)+0}{-3+0+0}$
$\to C = 0$
