a, \(\lim\limits_{x\rightarrow2}3x^2+7x+11=3.2^2+7.2+11=37\)
b, \(\lim\limits_{x\rightarrow2}\dfrac{x^2-4}{x-2}=\lim\limits_{x\rightarrow2}\dfrac{\left(x-2\right)\left(x+2\right)}{x-2}=\lim\limits_{x\rightarrow2}x+2=2+2=4\)
c, \(\lim\limits_{x\rightarrow2}\dfrac{x^2+3x-10}{3x^2-5x-2}=\lim\limits_{x\rightarrow2}\dfrac{\left(x-2\right)\left(x+5\right)}{\left(x-2\right)\left(3x+1\right)}=\lim\limits_{x\rightarrow2}\dfrac{x+5}{3x+1}=\dfrac{2+5}{3.2+1}=1\)
d, \(\lim\limits_{x\rightarrow1}\dfrac{2x-\sqrt{3x+1}}{x^2-1}=\lim\limits_{x\rightarrow1}\dfrac{4x^2-3x-1}{\left(x^2-1\right)\left(2x+\sqrt{3x+1}\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{\left(x-1\right)\left(4x+1\right)}{\left(x-1\right)\left(x+1\right)\left(2x+\sqrt{3x+1}\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{4x+1}{\left(x+1\right)\left(2x+\sqrt{3x+1}\right)}=\dfrac{4.1+1}{\left(1+1\right)\left(2.1+\sqrt{3.1+1}\right)}=\dfrac{5}{8}\)
