Đáp án:
1) -2
Giải thích các bước giải:
\(\begin{array}{*{20}{l}}
{1)\mathop {\lim }\limits_{x \to {\rm{ \;}} - 1} \frac{{{x^2} - x + 2 - 4}}{{\left( {x + 1} \right)\left( {x + 2} \right)\left( {\sqrt {{x^2} - x + 2} + 2} \right)}}}\\
{ = \mathop {\lim }\limits_{x \to {\rm{ \;}} - 1} \frac{{\left( {x + 1} \right)\left( {x - 2} \right)}}{{\left( {x + 1} \right)\left( {x + 2} \right)\left( {\sqrt {{x^2} - x + 2} + 2} \right)}}}\\
{ = \mathop {\lim }\limits_{x \to {\rm{ \;}} - 1} \frac{{x - 2}}{{\left( {x + 2} \right)\left( {\sqrt {{x^2} - x + 2} + 2} \right)}}}\\
{ = \frac{{ - 1 - 2}}{{\left( { - 1 + 2} \right)\left( {2 + 2} \right)}} = {\rm{ }}\frac{{ - 3}}{4}}\\
{ \to a = {\rm{ \;}}\frac{{ - 3}}{4}}\\
{ \to 4a + 1 = {\rm{ \;}} - 3 + 1 = {\rm{ \;}} - 2}\\
{2)\mathop {\lim }\limits_{x \to a} \frac{{{a^2} - \left( {a + 1} \right).a + a}}{{2{a^3}}}}\\
{ = \frac{{{a^2} - {a^2} - a + a}}{{2{a^3}}} = \frac{0}{{2{a^3}}} = 0}
\end{array}\)
