A number ‘l’ is called limit of a function f(x) when i.e., if given , there exists such that |x –a| | f(x) – l | < .
Right hand and left hand limits
Let h be a small positive number. Left hand side limit of f(x) when , is denoted by f(a -0) and is defined as:
Right hand side limit of f(x), when , is denoted by f(a + 0) and is defined as:
If a function f(x) takes the form , then say that f(x) is indeterminate at x=a. Other Indeterminate Forms are .
L’ hospital’s rule
If and are functions of x such that , then
This form can easily be reduced either to form of .
This can also be reduced to the form
Sandwich Theorem (or Squeeze principle)
If f, g, h are functions such that for all x in the neighborhood of a and if ,
Algebra of limits
Evaluation of exponential limits of the form
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