1.6 Calculating Limits Using the Limit Laws

1. Sum Law

$$
\lim_{x\to a}[f(x)+g(x)] = \lim_{x\to a}f(x) + \lim_{x\to a}g(x)
$$

2. Difference Law

$$
\lim_{x\to a}[f(x)-g(x)] = \lim_{x\to a}f(x) - \lim_{x\to a}g(x)
$$

3. Constant Multiple Law

$$
\lim_{x\to a}[cf(x)] = c\lim_{x\to a}f(x)
$$

4. Product Law

$$
\lim_{x\to a}[f(x)g(x)] = \lim_{x\to a}f(x) * \lim_{x\to a}g(x)
$$

5. Quotien Law

$$
\lim_{x\to a}{f(x) \over g(x)} = {\lim_{x\to a}f(x) \over \lim_{x\to a}g(x)}
\quad if \lim_{x\to a}g(x) \neq 0
$$

6. Power Law

$$
\lim_{x \to a}[f(x)]^n=[\lim_{x \to a}f(x)]^n
$$

$$
\lim_{x \to a}c=c
$$

$$
\lim_{x \to a}x=a
$$

$$
\lim_{x \to a}x^n=a^n
$$

$$
\lim_{x \to a}\sqrt[n] {x}=\sqrt[n] {a}
$$

$$
\lim_{x \to a}\sqrt[n] {f(x)}=\sqrt[n] {\lim_{f\to a}f(x)}
$$

• $$\lim_{x \to \pi} {sinx\over x}=1$$