Answer
(a)-6
(b)13
(c)-8
(d)16
(e)2
(f)-1/2
Work Step by Step
$(a)\lim\limits_{x \to a}[f(x)+2g(x)]=\lim\limits_{x \to a}[f(x)]+2\lim\limits_{x \to a}[g(x)]=2+2(-4)=2-8=-6\\
(b)\lim\limits_{x \to a}[h(x)-3g(x)+1]=\lim\limits_{x \to a}h(x)-3\lim\limits_{x \to a}g(x)+\lim\limits_{x \to a}(1)=0-3(-4)+1=12+1=13\\
(c)\lim\limits_{x \to a}[f(x)g(x)]=\lim\limits_{x \to a}[f(x)]*\lim\limits_{x \to a}[g(x)]=2*(-4)=-8\\
(d)\lim\limits_{x \to a}[g(x)]^{2}=[\lim\limits_{x \to a}g(x)]^{2}=(-4)^{2}=16\\
(e)\lim\limits_{x \to a}\sqrt[3] [6+f(x)]=\sqrt[3] [6+\lim\limits_{x \to a}[f(x)]=\sqrt[3] [6+2]=\sqrt[3] [8]=2\\
(f)\lim\limits_{x \to a}\frac{2}{g(x)}=\frac{2}{\lim\limits_{x \to a}[g(x)]}=\frac{2}{-4}=-\frac{1}{2}\\
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