graph the function. then use your graph to find the indicated limit. 36) f(x) = {x + 7 x < -7, 7 - x x ≥ -7…

Explanation:

Step1: Find left - hand limit

For (x < - 7), (f(x)=x + 7). (\lim_{x\rightarrow - 7^{-}}f(x)=\lim_{x\rightarrow - 7^{-}}(x + 7)) Substitute (x=-7) into (x + 7): (-7 + 7=0)

Step2: Find right - hand limit

For (x\geq - 7), (f(x)=7 - x). (\lim_{x\rightarrow - 7^{+}}f(x)=\lim_{x\rightarrow - 7^{+}}(7 - x)) Substitute (x = - 7) into (7 - x): (7-(-7)=14)

Step3: Check if limit exists

Since (\lim_{x\rightarrow - 7^{-}}f(x)=0) and (\lim_{x\rightarrow - 7^{+}}f(x)=14), (\lim_{x\rightarrow - 7^{-}}f(x)\neq\lim_{x\rightarrow - 7^{+}}f(x))

Answer:

The limit (\lim_{x\rightarrow - 7}f(x)) does not exist.