Let , defined for all real…

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

g(x)=\dfrac{3x+1}{x(x-4)}

, defined for all real

x\neq 0,4

. (a) Calculate

\displaystyle \lim_{x\to 0^{-}} g(x)

. Show all steps in your reasoning. (b) Calculate

\displaystyle \lim_{x\to 0^{+}} g(x)

. (c) Calculate

\displaystyle \lim_{x\to 4^{-}} g(x)

. (d) Calculate

\displaystyle \lim_{x\to 4^{+}} g(x)

. (e) Based on your results, list the equations of all vertical asymptotes of

g

and indicate on which side(s) the graph of

g

approaches

+\infty

and on which side(s) it approaches

-\infty

. Justify your conclusions.