Limits

Computing a limit just means computing what happens to the values of the function if f(x) is evaluated for values of x getting closer and closer to(but does not equal) the number c , if these values of f(x) get closer and closer to one particular number L . You say that The limit of f(x), as x approaches c, equals LAnd write

1.1 Properties of Limits

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1When the substitution in the limit yields we must simplified the limit then substitute.

Note

Example 1:

Example 2:

Example 3: Solution: Example4:

Solution:

A function (x) has a limit as x approaches c if and only if it has left-hand and right-hand limits there and these one-sided limits are equal:

Example: Show that Solution /

This type of function called exist

Example: prove that Solution / The function is not exist because Right-hand side not equal left hand side

Example: =Determine where there Solution /

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