Evaluate each limit.
$lim_{x \to - 3^{+}} f (x), f (x) = {\begin{cases} - x^{2} - 4 x - 5, & x < - 3 \\ \frac{x}{2} - 5, & x \geq - 3 \end{cases}$

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Answer

Final Answer: $- \frac{13}{2}$

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: $- \frac{13}{2}$