find the limits in a) through c) below for the function $f(x)=\frac{x^{2}-11x + 10}{x + 10}$. use $-infty$…

find the limits in a) through c) below for the function $f(x)=\frac{x^{2}-11x + 10}{x + 10}$. use $-infty$ and $infty$ when appropriate.\na) select the correct choice below and fill in any answer boxes in your choice.\na. $lim_{x\rightarrow - 10^{-}}f(x)=-infty$ (simplify your answer.)\nb. 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. $lim_{x\rightarrow - 10^{+}}f(x)=square$ (simplify your answer.)\nb. the limit does not exist and is neither $-infty$ nor $infty$.

find the limits in a) through c) below for the function $f(x)=\frac{x^{2}-11x + 10}{x + 10}$. use $-infty$ and $infty$ when appropriate.\na) select the correct choice below and fill in any answer boxes in your choice.\na. $lim_{x\rightarrow - 10^{-}}f(x)=-infty$ (simplify your answer.)\nb. 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. $lim_{x\rightarrow - 10^{+}}f(x)=square$ (simplify your answer.)\nb. the limit does not exist and is neither $-infty$ nor $infty$.

Answer

Explanation:

Step1: Factor the numerator

First, factor (x^{2}-11x + 10=(x - 10)(x - 1)). So (f(x)=\frac{(x - 10)(x - 1)}{x + 10}).

Step2: Analyze the left - hand limit as (x\to - 10^{-})

As (x\to - 10^{-}), the numerator ((x - 10)(x - 1)\to(-10 - 10)(-10 - 1)=(-20)\times(-11) = 220>0), and the denominator (x + 10\to0^{-}). So (\lim_{x\to - 10^{-}}f(x)=-\infty).

Step3: Analyze the right - hand limit as (x\to - 10^{+})

As (x\to - 10^{+}), the numerator ((x - 10)(x - 1)\to(-10 - 10)(-10 - 1)=220>0), and the denominator (x + 10\to0^{+}). So (\lim_{x\to - 10^{+}}f(x)=\infty).

Answer:

a) A. (\lim_{x\to - 10^{-}}f(x)=-\infty) b) A. (\lim_{x\to - 10^{+}}f(x)=\infty)