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Do Now: 1.Complete the table: 2.Why do you suppose you weren’t asked to evaluate f(4)? 3.Describe the behavior of the values in the f(x) column as the values in the x column get close to 4.

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Have you reached your limit? an introduction to limits and evaluating limits

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A limit problem asks, as x approaches some value, what does f(x) approach? Read “the limit as x approaches a of f(x) is what?”

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In a later lesson, you are going to learn some methods of evaluating limits. For the time being, you will use t-tables to help you evaluate limits. You were actually evaluating a limit in the “do now” activity:

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The table feature of a graphing utility is useful in evaluating limits. Calculator instructions: Go to the Y= screen and type in the function. Use 2 nd WINDOW (TBL SET) to set the start value at 3 and the step value (∆ Tbl) to 0.01. Use 2 nd GRAPH to view the table.

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Because polynomial functions are continuous and have all real numbers as their domain,

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A limit problem does NOT ask what happens when you evaluate a function at some x value. It asks what is happening as x approaches some value. A limit can exist x→a even when f(a) does not exist. From the “do now” activity:

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Limits can be evaluated from the left-hand, right-hand, or both directions: from the left: from the right:

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Some limits do not exist. In order for a limit to exist, the limit as x approaches some value from the left must equal the limit as x approaches that same x value from the right.

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DNE

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If f(x) increases without bound (goes to infinity) or decreases without bound (goes to negative infinity), then the limit does not exist. DNE

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Evaluate the limit: 1. 2. 3.

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Math 1304 Calculus I 2.2 – Limits Introduction.

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