Question

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:

\(0\)