lim_{x\\to -15^{+}}\\frac{x + 15}{\\sqrt{x + 15}}

Explanation:

Step1: Simplify the expression

Let (t = x + 15). As (x\to - 15^{+}), then (t\to0^{+}). The original limit (\lim_{x\to - 15^{+}}\frac{x + 15}{\sqrt{x + 15}}) becomes (\lim_{t\to0^{+}}\frac{t}{\sqrt{t}}). Since (\frac{t}{\sqrt{t}}=\sqrt{t}) for (t>0).

Step2: Evaluate the limit

We know that the function (y = \sqrt{t}) is continuous for (t\geq0). Using the property of continuous - function (\lim_{t\to a}f(t)=f(a)) (when (f(t)) is continuous at (t = a)), for (f(t)=\sqrt{t}) and (a = 0). (\lim_{t\to0^{+}}\sqrt{t}=0)

Answer:

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