# Chapter 1 - Limits and Their Properties - 1.3 Exercises: 40

a) $3.$ b) $\frac{3}{2}.$ c) $729.$ d) $9.$

#### Work Step by Step

Using Theorem $1.2$ and Theorem $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)):$ a) $\lim\limits_{x\to c}\sqrt[3]{f(x)}=\sqrt[3]{\lim\limits_{x\to c}f(x)}=\sqrt[3]{27}=3.$ b) $\lim\limits_{x\to c}\dfrac{f(x)}{18}=\dfrac{\lim\limits_{x\to c}f(x)}{\lim\limits_{x\to c}(18)}=\dfrac{27}{18}=\dfrac{3}{2}.$ c)$\lim\limits_{x\to c}[f(x)]^2=[\lim\limits_{x\to c}f(x)]^2=27^2=729.$ d) $\lim\limits_{x\to c}[f(x)]^{\frac{2}{3}}=[\lim\limits_{x\to c}f(x)]^{\frac{2}{3}}=27^{\frac{2}{3}}=9.$

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