Question

lim x→∞ √x²+x(2a+2b)+4ab-x
notice : all coefficients and variables are in the root
AND IF YOU CAN'T ANSWER, DON'T ANSWER THIS QUESTION!!!!!​
( WITH THE STEPS!)

Answer 1

$\lim \limits_{x \to \infty} \sqrt{x^2 +x(2a+2b) +4ab-x}\\\\\\=\lim \limits_{x \to \infty} \sqrt{x^2 \left( 1 + \dfrac{2a+2b}{x}+ \dfrac{4ab}{x^2} - \dfrac 1{x} \right)}\\\\\\=\sqrt{\lim \limits_{x \to \infty} x^2 \cdot \lim \limits_{x \to \infty} \left( 1 + \dfrac{2a+2b}{x}+ \dfrac{4ab}{x^2} - \dfrac 1{x} \right)}}\\\\\\=\sqrt{ \infty \cdot (1+0+0-0)}\\\\=\sqrt{ \infty \cdot 1}\\\\=\infty$