Functions Limits and Continuity Summary


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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.


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