for the given piece - wise function, use properties of limits to find the indicated limit, or state that the…

for the given piece - wise function, use properties of limits to find the indicated limit, or state that the limit does not exist. a. lim f(x) b. lim f(x) c. lim f(x) x→3⁻ x→3⁺ x→3 f(x)={x + 6 if x<3; x + 7 if x≥3} a. find lim f(x). select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→3⁻ a. lim f(x)= (simplify your answer.) x→3⁻ b. lim f(x) does not exist x→3⁻

for the given piece - wise function, use properties of limits to find the indicated limit, or state that the limit does not exist. a. lim f(x) b. lim f(x) c. lim f(x) x→3⁻ x→3⁺ x→3 f(x)={x + 6 if x<3; x + 7 if x≥3} a. find lim f(x). select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→3⁻ a. lim f(x)= (simplify your answer.) x→3⁻ b. lim f(x) does not exist x→3⁻

Answer

Explanation:

Step1: Identify the function for $x\to3^{-}$

For $x\to3^{-}$, we use the part of the piece - wise function where $x < 3$. The function is $f(x)=x + 6$.

Step2: Calculate the left - hand limit

We find $\lim_{x\to3^{-}}f(x)$ by substituting $x = 3$ into $x + 6$. So, $\lim_{x\to3^{-}}f(x)=\lim_{x\to3^{-}}(x + 6)=3+6$.

Answer:

9