find the limits in a), b), and c) below for the function f(x) = \\frac{7x}{x - 3}. use -\\infty and \\infty…

find the limits in a), b), and c) below for the function f(x) = \\frac{7x}{x - 3}. use -\\infty and \\infty when appropriate.\na) \\(\\lim_{x\\to3^{-}}f(x)\n(simplify your answer.)\no b. the limit does not exist and is neither -\\infty nor \\infty.\nb) select the correct choice below and fill in any answer boxes in your choice.\na. \\(\\lim_{x\\to3^{+}}f(x)=\\infty\n(simplify your answer.)\no b. the limit does not exist and is neither -\\infty nor \\infty.\nc) select the correct choice below and fill in any answer boxes in your choice.\na. \\(\\lim_{x\\to3}f(x)= \n(simplify your answer.)\no 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{7x}{x - 3}. use -\\infty and \\infty when appropriate.\na) \\(\\lim_{x\\to3^{-}}f(x)\n(simplify your answer.)\no b. the limit does not exist and is neither -\\infty nor \\infty.\nb) select the correct choice below and fill in any answer boxes in your choice.\na. \\(\\lim_{x\\to3^{+}}f(x)=\\infty\n(simplify your answer.)\no b. the limit does not exist and is neither -\\infty nor \\infty.\nc) select the correct choice below and fill in any answer boxes in your choice.\na. \\(\\lim_{x\\to3}f(x)= \n(simplify your answer.)\no b. the limit does not exist and is neither -\\infty nor \\infty.

Answer

Explanation:

Step1: Analyze left - hand limit as $x\to3^{-}$

As $x\to3^{-}$, $x - 3\to0^{-}$ (a very small negative number), and $7x\to21$. So, $\lim_{x\to3^{-}}\frac{7x}{x - 3}=-\infty$.

Step2: Analyze right - hand limit as $x\to3^{+}$

As $x\to3^{+}$, $x - 3\to0^{+}$ (a very small positive number), and $7x\to21$. So, $\lim_{x\to3^{+}}\frac{7x}{x - 3}=\infty$.

Step3: Analyze two - sided limit as $x\to3$

Since $\lim_{x\to3^{-}}f(x)=-\infty$ and $\lim_{x\to3^{+}}f(x)=\infty$, the two - sided limit $\lim_{x\to3}f(x)$ does not exist.

Answer:

a) $-\infty$ b) $\infty$ c) B. The limit does not exist and is neither $-\infty$ nor $\infty$.