Giải thích các bước giải:
\(\begin{array}{l}
1,\\
\mathop {\lim }\limits_{x \to 3} \left( {5{x^2} - 7x} \right) = {5.3^2} - 7.3 = 24\\
2,\\
\mathop {\lim }\limits_{x \to - 1} \frac{{{x^2} + 5}}{{x + 5}} = \frac{{{{\left( { - 1} \right)}^2} + 5}}{{\left( { - 1} \right) + 5}} = \frac{6}{4} = \frac{3}{2}\\
3,\\
\mathop {\lim }\limits_{x \to 3} \frac{{{x^2} + 2x - 15}}{{x - 3}} = \mathop {\lim }\limits_{x \to 3} \frac{{\left( {x + 5} \right)\left( {x - 3} \right)}}{{x - 3}} = \mathop {\lim }\limits_{x \to 3} \left( {x + 5} \right) = 3 + 5 = 8\\
4,\\
\mathop {\lim }\limits_{x \to - 1} \frac{{2{x^2} + 3x + 1}}{{{x^2} - 1}} = \mathop {\lim }\limits_{x \to - 1} \frac{{\left( {2x + 1} \right)\left( {x + 1} \right)}}{{\left( {x - 1} \right)\left( {x + 1} \right)}} = \mathop {\lim }\limits_{x \to - 1} \frac{{2x + 1}}{{x - 1}} = \frac{{2.\left( { - 1} \right) + 1}}{{\left( { - 1} \right) - 1}} = \frac{1}{2}
\end{array}\)
