Answer
(a) Quotient Rule.
(b) Numerator: Difference Rule - Denominator: Power Rule
(c) Numerator: Constant Multiple Rule - Denominator: Sum Rule
Work Step by Step
(a) $\lim\limits_{x\to c}\dfrac{p}{q}$ to $\dfrac{\lim\limits_{x\to c} p}{\lim\limits_{x\to c} q}$. This is defined as Quotient Rule.
(b) In the numerator: $\lim_\limits{x\to c}(p-q)=\lim\limits_{x\to c}p-\lim_{x\to c}q$. This is Difference Rule.
and in the denominator: $\lim_\limits{x\to c}(p^n)=(\lim\limits_{x\to c}p)^n$. The Power Rule is applied.
(c) In the numerator $\lim\limits_{x\to0}nf(x)=n\lim\limits_{x\to0}f(x)$. The Constant Multiple Rule is applied.
and in the denominator: $\lim\limits_{x\to c}(p+q)=\lim\limits_{x\to c}p+\lim\limits_{x\to c}q$. The Sum Rule is applied.
