Functions Limits and Continuity Summary

 

Algebra of limits

Step I:

Factor of f(x) and g(x).

Step II:

Common factors of numerator and denominator are

Step III:

Substitute x = a and obtain the limits.

Standard Results

Limits at infinity and infinite limits:

Infinite limit of a function:

• If f(x) can be made as small as possible (negatively infinite) as x ® a we say

• A real function f(x) is said to be continuous at x = a, if

(i) f(a) is defined

• If f₁ and f₂ are continuous functions, then

• Every polynomial is continuous.

• Every rational function is continuous.