find the limits in a), b), and c) below for the function (f(x)=\frac{5x}{x - 6}). use (-infty) and (infty)…

find the limits in a), b), and c) below for the function (f(x)=\frac{5x}{x - 6}). use (-infty) and (infty) when appropriate. a) select the correct choice below and fill in any answer boxes in your choice. (lim_{x\rightarrow6^{-}}f(x)=) (simplify your answer.) a. (-infty) b. the limit does not exist and is neither (-infty) nor (infty). b) select the correct choice below and fill in any answer boxes in your choice. (lim_{x\rightarrow6^{+}}f(x)=) (simplify your answer.) a. (infty) b. the limit does not exist and is neither (-infty) nor (infty).

find the limits in a), b), and c) below for the function (f(x)=\frac{5x}{x - 6}). use (-infty) and (infty) when appropriate. a) select the correct choice below and fill in any answer boxes in your choice. (lim_{x\rightarrow6^{-}}f(x)=) (simplify your answer.) a. (-infty) b. the limit does not exist and is neither (-infty) nor (infty). b) select the correct choice below and fill in any answer boxes in your choice. (lim_{x\rightarrow6^{+}}f(x)=) (simplify your answer.) a. (infty) b. the limit does not exist and is neither (-infty) nor (infty).

Answer

Explanation:

Step1: Analyze the function for (x\rightarrow6^{-})

The function is (f(x)=\frac{5x}{x - 6}). When (x\rightarrow6^{-}), the numerator (5x\rightarrow30) and the denominator (x - 6\rightarrow0^{-}). So (\lim_{x\rightarrow6^{-}}f(x)=-\infty).

Step2: Analyze the function for (x\rightarrow6^{+})

When (x\rightarrow6^{+}), the numerator (5x\rightarrow30) and the denominator (x - 6\rightarrow0^{+}). So (\lim_{x\rightarrow6^{+}}f(x)=\infty).

Answer:

a) A. (\lim_{x\rightarrow6^{-}}f(x)=-\infty) b) A. (\lim_{x\rightarrow6^{+}}f(x)=\infty)