c) lim _{x rightarrow 2} frac{sqrt[3]{(x+6)}-2}{x-2} cdot frac{sqrt[3]{(x+6)}+2}{sqrt[3]{(x+6)}+2}

Question

Accepted Answer

Step:1 ：(text{Simplify the expression by multiplying the two fractions:})Step:2 ：(frac{sqrt[3]{(x+6)}-2}{x-2} cdot frac{sqrt[3]{(x+6)}+2}{sqrt[3]{(x+6)}+2} = frac{(sqrt[3]{(x+6)}-2)(sqrt[3]{(x+6)}+2)}{x-2})Step:3 ：(text{Find the limit as x approaches 2:})Step:4 ：(lim_{x rightarrow 2} frac{(sqrt[3]{(x+6)}-2)(sqrt[3]{(x+6)}+2)}{x-2})Step:5 ：(text{The limit as x approaches 2 is infinity.})Step:6 ：(boxed{infty})

Answer

Step: 1 ：(text{Simplify the expression by multiplying the two fractions:})Step: 2 ：(frac{sqrt[3]{(x+6)}-2}{x-2} cdot frac{sqrt[3]{(x+6)}+2}{sqrt[3]{(x+6)}+2} = frac{(sqrt[3]{(x+6)}-2)(sqrt[3]{(x+6)}+2)}{x-2})Step: 3 ：(text{Find the limit as x approaches 2:})Step: 4 ：(lim_{x rightarrow 2} frac{(sqrt[3]{(x+6)}-2)(sqrt[3]{(x+6)}+2)}{x-2})Step: 5 ：(text{The limit as x approaches 2 is infinity.})Step: 6 ：(boxed{infty})

c) $\lim _{x \rightarrow 2} \frac{\sqrt[3]{(x+6)}-2}{x-2} \cdot \frac{\sqrt[3]{(x+6)}+2}{\sqrt[3]{(x+6)}+2}$

Answer

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