Question

Tính:

a) \(\mathop {\lim }\limits_{x \to 2} \left[ {\left( {x + 1} \right)\left( {{x^2} + 2x} \right)} \right];\)                         

b) \(\mathop {\lim }\limits_{x \to 2} \sqrt {{x^2} + x + 3} .\)

Answer 1

a) \(\mathop {\lim }\limits_{x \to 2} \left[ {\left( {x + 1} \right)\left( {{x^2} + 2x} \right)} \right] = \mathop {\lim }\limits_{x \to 2} \left( {x + 1} \right).\mathop {\lim }\limits_{x \to 2} \left( {{x^2} + 2x} \right) = \left( {2 + 1} \right).\left( {{2^2} + 2.2} \right) = 24\)                

b) \(\mathop {\lim }\limits_{x \to 2} \sqrt {{x^2} + x + 3}  = \sqrt {\mathop {\lim }\limits_{x \to 2} \left( {{x^2} + x + 3} \right)}  = \sqrt {\mathop {\lim }\limits_{x \to 2} {x^2} + \mathop {\lim }\limits_{x \to 2} x + \mathop {\lim }\limits_{x \to 2} 3}  = \sqrt {{2^2} + 2 + 3}  = 3\)