Question

next, we check the limit when approaching from the right. as x approaches -6 from the right, we have
lim(x→ - 6⁺) (5x + 30)/|x + 6| = lim(x→ - 6⁺) (5x + 30)/i

Explanation:

Step1: Analyze the absolute - value function

When \(x\to - 6^{+}\), \(x+6>0\), so \(|x + 6|=x + 6\).

Step2: Rewrite the limit

\(\lim_{x\to - 6^{+}}\frac{5x + 30}{|x + 6|}=\lim_{x\to - 6^{+}}\frac{5x + 30}{x + 6}\).
Factor the numerator: \(5x+30 = 5(x + 6)\).
So \(\lim_{x\to - 6^{+}}\frac{5(x + 6)}{x + 6}\).

Step3: Simplify the expression

Cancel out the common factor \((x + 6)\) (since \(x
eq - 6\) when taking the limit), we get \(\lim_{x\to - 6^{+}}5=5\).

Answer:

5