a piecewise function is given. use properties of limits to find the indicated limits, or state that a limit…

a piecewise function is given. use properties of limits to find the indicated limits, or state that a limit does not exist. f(x) = { (x² - 49)/(x - 7) x≠7; 1 x = 7. a. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x) = (type an integer or a simplified fraction.) x→7⁻ b. the limit does not exist.

a piecewise function is given. use properties of limits to find the indicated limits, or state that a limit does not exist. f(x) = { (x² - 49)/(x - 7) x≠7; 1 x = 7. a. select the correct choice below and fill in any answer boxes in your choice. a. lim f(x) = (type an integer or a simplified fraction.) x→7⁻ b. the limit does not exist.

Answer

Explanation:

Step1: Simplify the function for x≠7

For (x\neq7), factor (x^{2}-49=(x + 7)(x - 7)). So (f(x)=\frac{x^{2}-49}{x - 7}=\frac{(x + 7)(x - 7)}{x - 7}=x + 7).

Step2: Find the left - hand limit

To find (\lim_{x\rightarrow7^{-}}f(x)), we use the simplified form (f(x)=x + 7) (since for (x\rightarrow7^{-}), (x\neq7)). Substitute (x = 7) into (x+7). We get (\lim_{x\rightarrow7^{-}}f(x)=\lim_{x\rightarrow7^{-}}(x + 7)=7+7 = 14).

Answer:

A. (\lim_{x\rightarrow7^{-}}f(x)=14)