Limit of a function at a Point. Example 1 Consider the function f(x)=x 2 on the domain (-1,4].

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Presentation transcript:

Limit of a function at a Point

Example 1 Consider the function f(x)=x 2 on the domain (-1,4].

Exercise 1 Calculate the following limits using the " " notation. In case the limit does not exist (DNE) indicate the reason.

LIMIT OF A FUNCTION AT A POINT The expression, L a number, means that no matter the direction through which the x values approach a, the heights or values of the function y=f(x), are getting infinitely close to L.

Exercise 4 Evaluate the following limits

Limits at Infinity For each of the following functions make a conjecture about. Explain in words your conjecture.

LIMITS AT INFINITY, L a real number, if for any sequence. Likewise,, M a real number, if for any sequence When one of the limits above exists, the function is said to have a Horizontal Asymptote at either y=L or y=M.

End Behavior of Basic Functions Verify the end behavior of the following functions using sequences. Then use “ “ notation

Dominance of Functions As (a could be infinity or negative infinity) the function y=f(x) dominates the function y=g(x), if These conditions are equivalent to saying

If the function y=f(x) dominates the function y=g(x) as, In other words, in terms of the limiting process the function g(x) becomes insignificant.

Determine the form of the following limits and calculate them. In case of “trouble-makers” indicate how to resolve it.

Using Dominance to Evaluate Limits