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\\to - 10^{-}}f(x)=\\square\n(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\\to - 10^{-}}f(x)=\\square\n(simplify your answer.)\nb. the limit does not exist and is neither -\\infty nor \\infty.

Answer

Explanation:

Step1: Factor the numerator

Factor $x^{2}-11x + 10$ as $(x - 10)(x - 1)$. So $f(x)=\frac{(x - 10)(x - 1)}{x + 10}$.

Step2: Analyze the left - hand limit

As $x\to - 10^{-}$, we consider values of $x$ that are slightly less than $-10$. The numerator $(x - 10)(x - 1)$ approaches $(-10-10)(-10 - 1)=(-20)\times(-11)=220$. The denominator $x + 10$ approaches a small negative number.

Step3: Calculate the limit

Since the numerator is a non - zero constant and the denominator approaches $0$ from the negative side, $\lim_{x\to - 10^{-}}\frac{(x - 10)(x - 1)}{x + 10}=-\infty$.

Answer:

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