Question

lim ( \(\sqrt{x^2+100}+x\)) 

x-> -∞

Answer 1

\(\mathop {\lim }\limits_{x \to - \infty } \left( {\sqrt {{x^2} + 100} + x} \right) = \mathop {\lim }\limits_{x \to - \infty } \dfrac{{\left( {\sqrt {{x^2} + 100} + x} \right)\left( {\sqrt {{x^2} + 100} - x} \right)}}{{\sqrt {{x^2} + 100} - x}} = \mathop {\lim }\limits_{x \to - \infty } \dfrac{{100}}{{ - x\sqrt {1 + \dfrac{{100}}{x} - x} }} = \mathop {\lim }\limits_{x \to - \infty } \dfrac{{\dfrac{{100}}{x}}}{{ - \sqrt {1 + \dfrac{{100}}{x} - 1} }} = 0\)