Question

for the function g(x) shown below, compute the following limits or state that they do not exist.
g(x) = \begin{cases} 0 & \text{if } x leq -5 \\sqrt{25 - x^2} & \text{if } -5 < x < 5 \\ 2x & \text{if } x geq 5 end{cases}

a. (limlimits_{x \to -5^-} g(x)) b. (limlimits_{x \to -5^+} g(x)) c. (limlimits_{x \to -5} g(x)) d. (limlimits_{x \to 5^-} g(x)) e. (limlimits_{x \to 5^+} g(x)) f. (limlimits_{x \to 5} g(x))

(\boldsymbol{x \to 5^-})

a. (limlimits_{x \to 5^-} g(x) = 0)
b. the limit does not exist.

e. find (limlimits_{x \to 5^+} g(x)) select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. (limlimits_{x \to 5^+} g(x) = square)
b. the limit does not exist.

Explanation:

Part e: $\lim_{x \to 5^+} g(x)$

Step1: Determine the relevant piece

For $x \to 5^+$, we use the piece where $x \geq 5$, so $g(x) = 2x$.

Step2: Evaluate the limit

Substitute $x = 5$ into $2x$: $\lim_{x \to 5^+} 2x = 2(5) = 10$.

Answer:

A. $\lim_{x \to 5^+} g(x) = 10$