| Quick Tour Find the following limits. Be sure to explain your reasoning at every step. \begin{alignat*}{3} &a) \lim_{x \to \infty}\frac{x+\sin x }{ 5x+6} & &b) \lim_ {x \to \infty}\frac{\sin x }{ x} & &c) \lim_{x \to \infty}x \sin \frac{ 1 }{ x} \\ &d) \lim_{x \to \infty}\frac{x \sin x }{ x^2+5} & &e) \lim_{x \to \infty}{\sqrt {x^2+x} - x} & &f) \lim_{x \to \infty}\frac{x^2( 1+ \sin^2x) }{ (x+\sin x )^2} \end{alignat*} |