a. \(\mathop {\lim }\limits_{x \to \sqrt 3 } \left| {{x^2} - 8} \right| = \left| {{{\left( {\sqrt 3 } \right)}^2} - 8} \right| = 5\)
b. \(\mathop {\lim }\limits_{x \to 2} {{{x^2} + x + 1} \over {{x^2} + 2x}} = {{{2^2} + 2 + 1} \over {{2^2} + 2.2}} = {7 \over 8}\)
c. \(\mathop {\lim }\limits_{x \to - 1} \sqrt {{{{x^3}} \over {{x^2} - 3}}} = \sqrt {{1 \over 2}} = {{\sqrt 2 } \over 2}\)
d. \(\mathop {\lim }\limits_{x \to 3} \root 3 \of {{{2x\left( {x + 1} \right)} \over {{x^2} - 6}}} = \root 3 \of {{{24} \over 3}} = 2\)
e. \(\mathop {\lim }\limits_{x \to - 2} {{\sqrt {1 - {x^3}} - 3x} \over {2{x^2} + x - 3}} = {{3 + 6} \over {8 - 5}} = 3\)
f. \(\mathop {\lim }\limits_{x \to - 2} {{2\left| {x + 1} \right| - 5\sqrt {{x^2} - 3} } \over {2x + 3}} = {{2 - 5} \over { - 4 + 3}} = 3\)
