Answer
(a) Quotient Rule.
(b) Numerator: Root Rule - Denominator: Product Rule
(c) Numerator: Constant Multiple Rule - Denominator: Difference Rule
Work Step by Step
(a) $\lim_{x\to1}\frac{\sqrt{5h(x)}}{p(x)(4-r(x))}=\dfrac{\lim_{x\to1}\sqrt{5h(x)}}{\lim_{x\to1}(p(x)(4-r(x)))}$
Here, $\lim_{x\to c}\dfrac{p}{q}=\dfrac{\lim_{x\to c}p}{\lim_{x\to c}q}$. The Quotient Rule is applied.
(b) In the numerator we have $\lim_{x\to c}\sqrt[n]p=\sqrt[n]{\lim_{x\to c}p}$. The Root Rule is applied.
and in the denominator: $\lim_{x\to c}(pq)=\lim\limits_{x\to c}p\times\lim\limits_{x\to c}q$. The Product Rule is applied.
(c) Here, in the numerator: $\lim_{x\to c}(np)=n\lim_{x\to c}p$. The Constant Multiple Rule is applied and in the denominator we have $\lim_{x\to1}(4-r(x))=\lim_{x\to1}4-\lim_{x\to1}r(x)$. The Difference Rule is applied.
