evaluate the limits. if any of them tend towards $-\\infty$ or $+\\infty$, enter \oo\ (two lower case \o\…

evaluate the limits. if any of them tend towards $-\\infty$ or $+\\infty$, enter \oo\ (two lower case \o\ letters) for the infinity symbol. if the limit does not exist, enter \dne\.\n\n$\\lim_{x\\to3^{-}}\\frac{7}{x - 3}=$\n\n$\\lim_{x\\to3^{+}}\\frac{7}{x - 3}=$\n\n$\\lim_{x\\to3}\\frac{7}{x - 3}=$

evaluate the limits. if any of them tend towards $-\\infty$ or $+\\infty$, enter \oo\ (two lower case \o\ letters) for the infinity symbol. if the limit does not exist, enter \dne\.\n\n$\\lim_{x\\to3^{-}}\\frac{7}{x - 3}=$\n\n$\\lim_{x\\to3^{+}}\\frac{7}{x - 3}=$\n\n$\\lim_{x\\to3}\\frac{7}{x - 3}=$

Answer

Explanation:

Step1: Analyze ( \lim_{x\rightarrow3^{-}}\frac{7}{x - 3} )

When ( x\rightarrow3^{-} ), ( x-3\rightarrow0^{-} ). So ( \frac{7}{x - 3}\rightarrow-\infty )

Step2: Analyze ( \lim_{x\rightarrow3^{+}}\frac{7}{x - 3} )

When ( x\rightarrow3^{+} ), ( x - 3\rightarrow0^{+} ). So ( \frac{7}{x - 3}\rightarrow+\infty )

Step3: Analyze ( \lim_{x\rightarrow3}\frac{7}{x - 3} )

Since ( \lim_{x\rightarrow3^{-}}\frac{7}{x - 3}\neq\lim_{x\rightarrow3^{+}}\frac{7}{x - 3} ), the two - sided limit does not exist.

Answer:

(-\text{oo}) (+\text{oo}) (\text{DNE})