2. $lim_{x\rightarrow5}sqrt{3x - 11}$ 3. $lim_{x\rightarrow0}(-5)$
2. $lim_{x\rightarrow5}sqrt{3x - 11}$ 3. $lim_{x\rightarrow0}(-5)$
Answer
Explanation:
Step1: Substitute the value of x
We use the direct - substitution property of limits. If (y = f(x)) is continuous at (x = a), then (\lim_{x\rightarrow a}f(x)=f(a)). The function (y = \sqrt{3x - 11}) is continuous for (3x-11\geq0). When (x = 5), we substitute (x = 5) into (\sqrt{3x - 11}). (\sqrt{3\times5 - 11})
Step2: Simplify the expression
First, calculate the value inside the square - root: (3\times5-11=15 - 11 = 4). Then, (\sqrt{4}=2). For (\lim_{x\rightarrow0}(- 5)), since the function (y=-5) is a constant function, and for a constant function (y = c), (\lim_{x\rightarrow a}c=c) for any real number (a). So (\lim_{x\rightarrow0}(-5)=-5).
Answer:
(\lim_{x\rightarrow5}\sqrt{3x - 11}=2), (\lim_{x\rightarrow0}(-5)=-5)