Transcription of 11 Limits and an Introduction to Calculus - Cengage
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11 Limits and an Introduction to Calculus - Cengage
749 Limits and an Introductionto Introduction to Techniques for Evaluating The Tangent Line Limits at Infinity and Limits of The Area Problem110100,00006 Section , Example 3 Average 11 Limits and an Introduction to CalculusThe Limit ConceptThe notion of a limit is a fundamentalconcept of Calculus . In this chapter, you will learnhow to evaluate Limits and how they are used in the two basic problems of Calculus : thetangent line problem and the area 1 Finding a Rectangle of Maximum AreaYou are given 24 inches of wire and are asked to form a rectangle whose area is as largeas possible. What dimensions should the rectangle have?SolutionLet represent the width of the rectangle and let represent the length of the is follows that as shown in Figure So, the area of the rectangle isFormula for areaSubstitute for this model for area, you can experiment with different values of to see how toobtain the maximum area.
752 Chapter 11 Limits and an Introduction to Calculus In Example 3, note that has a limit as even though the function is not defined at This often happens, and it is important to realize that the existence or nonexistence of at has no bearing on the existence of the limit of as
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