find the limit.\n\n$$\\lim_{x \\to 2} \\frac{x + 7}{x + 9}$$\n\nselect the correct choice below and, if…

find the limit.\n\n$$\\lim_{x \\to 2} \\frac{x + 7}{x + 9}$$\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. $$\\lim_{x \\to 2} \\frac{x + 7}{x + 9}=$$ (simplify your answer.)\nb. the limit does not exist.

find the limit.\n\n$$\\lim_{x \\to 2} \\frac{x + 7}{x + 9}$$\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. $$\\lim_{x \\to 2} \\frac{x + 7}{x + 9}=$$ (simplify your answer.)\nb. the limit does not exist.

Answer

Explanation:

Step1: Substitute (x = 2) into the function

We use the direct - substitution property for limits. If (f(x)=\frac{x + 7}{x+9}), then (\lim_{x\rightarrow a}f(x)=f(a)) when (f(a)) is well - defined. Substitute (x = 2) into (\frac{x + 7}{x+9}), we get (\frac{2+7}{2 + 9}).

Step2: Simplify the expression

Calculate the numerator (2 + 7=9) and the denominator (2+9 = 11). So, (\frac{2+7}{2 + 9}=\frac{9}{11}).

Answer:

A. (\lim_{x\rightarrow2}\frac{x + 7}{x+9}=\frac{9}{11})