Evaluate each limit.
\[
\lim _{x \rightarrow-3^{+}} f(x), f(x)=\left\{\begin{array}{ll}
-x^{2}-4 x-5, & x< -3 \\
\frac{x}{2}-5, & x \geq-3
\end{array}\right.
\]

Answer

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Answer

Final Answer: \(\boxed{-\frac{13}{2}}\)

Steps

Step 1 ：The limit as x approaches -3 from the right is asking for the value of the function as x gets very close to -3, but is still greater than -3.

Step 2 ：Since x is greater than -3, we should use the second part of the piecewise function to evaluate the limit.

Step 3 ：Substitute x = -3 into the function \(f = \frac{x}{2} - 5\).

Step 4 ：The limit as x approaches -3 from the right of the function f(x) is -13/2.

Step 5 ：Final Answer: \(\boxed{-\frac{13}{2}}\)