91Ó°ÊÓ

Find each of the right-hand and left-hand limits or state that they do not exist. $$ \lim _{x \rightarrow 1^{-}} \frac{\sqrt{1+x}}{4+4 x} $$

GC In Problems \(43-48,\) find the horizontal and vertical asymptotes for the graphs of the indicated functions. Then sketch their graphs. $$ F(x)=\frac{2 x}{x-3} $$

In Problems \(41-48\), determine whether the function is continuous at the given point \(c\). If the function is not continuous, determine whether the discontinuity is removable or nonremovable. $$ g(x)=\left\\{\begin{array}{cl} \frac{\sin x}{x}, & x \neq 0 \\ 0, & x=0 \end{array}\right. $$

Find each of the following limits or state that it does not exist. (a) \(\lim _{x \rightarrow 0^{+}} x[1 / x]\) (b) \(\lim _{x \rightarrow 0^{+}} x^{2}[1 / x]\) (c) \(\lim _{x \rightarrow 3^{-}}([x]+[-x])\) (d) \(\lim _{x \rightarrow 3^{+}}([x]+[-x])\)

In Problems \(41-48\), determine whether the function is continuous at the given point \(c\). If the function is not continuous, determine whether the discontinuity is removable or nonremovable. $$ F(x)=x \sin \frac{1}{x} ; c=0 $$

GC In Problems \(43-48,\) find the horizontal and vertical asymptotes for the graphs of the indicated functions. Then sketch their graphs. $$ F(x)=\frac{2 x}{x-3} $$

In Problems \(41-48\), determine whether the function is continuous at the given point \(c\). If the function is not continuous, determine whether the discontinuity is removable or nonremovable. $$ f(x)=\sin \frac{1}{x} ; c=0 $$

Find each of the right-hand and left-hand limits or state that they do not exist. $$ \lim _{x \rightarrow 0^{-}} \frac{x}{|x|} $$

GC In Problems \(43-48,\) find the horizontal and vertical asymptotes for the graphs of the indicated functions. Then sketch their graphs. $$ g(x)=\frac{2 x}{\sqrt{x^{2}+5}} $$

In Problems \(41-48\), determine whether the function is continuous at the given point \(c\). If the function is not continuous, determine whether the discontinuity is removable or nonremovable. $$ f(x)=\frac{4-x}{2-\sqrt{x}} ; c=4 $$