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exploration5

# exploration5 - Explorations 5 Introduction to Limits 1 Plot...

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Explorations 5 Introduction to Limits 1. Plot on your calculator the graph of this function. f(x) = x 3 - 7x 2 + 17x - 15 x - 3 Use a friendly window with x = 3 as a grid point. Sketch the results here. Show the behavior of the function in a neighborhood of x = 3. 2. Substitute 3 for x in the equation for f(x). What form does the answer take? What name is given to an expression of this form? 3. The graph of f has a removable discontinuity at x = 3. The y-value at this discontinuity is the limit of f(x) as x approaches 3. What number does this limit equal? 4. Make a table of values of f(x) for each 0.1 unit change in x-values from 2.5 through 3.5. 5. Between what two numbers does f(x) stay when x is kept in the open interval (2.5, 3.5)? 6. Simplify the fraction for f(x). Solve numerically to find the two numbers close to 3 between which x must be kept if f(x) is to stay between 1.99 and 2.01. 7. How far from x = 3 (to the left and to the right) are the two x-values in Problem 6? 8. For the statement “If x is within _______ units of 3 (but not equal to 3), then f(x) is within 0.01 unit of 2,” write the largest number that can go in the blank.

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exploration5 - Explorations 5 Introduction to Limits 1 Plot...

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