Calculating Limits Using The Limit Laws

Flashcards summarizing the key concepts and formulas for calculating limits using limit laws.

Limit Laws

Rules that are used to calculate limits of functions as they approach a specific value.

     1) lim [f(x) + g(x)]

lim f(x) + lim g(x) when both limits exist.

2) lim [f(x) - g(x)]

lim f(x) - lim g(x) when both limits exist.

3) lim [f(x)]^n

(lim f(x))^n, where n is a positive integer.

4) lim [f(x) * g(x)]

lim f(x) * lim g(x) when both limits exist.

5) lim [C]

C, where C is a constant.

6) lim [x]

a, as x approaches a.

7) lim [x^n]

a^n, where n is a positive integer.

The Squeeze Theorem

If f(x) ≤ g(x) ≤ h(x), then lim f(x) = lim g(x) = lim h(x) = L.

Constant Limit

The limit of a constant C as x approaches a is C.

Limit of x as x approaches a

The limit of x as x approaches a is a.

Limit of x raised to n as x approaches a

The limit is a raised to n, where n is a positive integer.