it: $$ lim _ { x \rightarrow - 15 ^ { + } } \frac { 2 x + 30 } { sqrt { x + 15 } } $$
it: $$ lim _ { x \rightarrow - 15 ^ { + } } \frac { 2 x + 30 } { sqrt { x + 15 } } $$
Answer
Explanation:
Step1: Factor the numerator
Factor out (2) from (2x + 30), we get (2(x + 15)). So the limit becomes (\lim_{x\rightarrow - 15^{+}}\frac{2(x + 15)}{\sqrt{x + 15}}).
Step2: Simplify the expression
Let (t=x + 15). As (x\rightarrow - 15^{+}), (t\rightarrow0^{+}). The expression (\frac{2(x + 15)}{\sqrt{x + 15}}=\frac{2t}{\sqrt{t}}) ((t>0)). Since (\frac{2t}{\sqrt{t}}=2\sqrt{t}) for (t>0).
Step3: Evaluate the limit
Now we find (\lim_{t\rightarrow0^{+}}2\sqrt{t}). Substitute (t = 0) into (2\sqrt{t}), we know that (\lim_{t\rightarrow0^{+}}2\sqrt{t}=0).
Answer:
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