 # Use the dividing out technique to evaluate limits of functions

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 tarix 20.09.2018 ölçüsü 0,64 Mb. #70010 • ## Use technology to approximate limits of functions graphically and numerically • ## Evaluate limits of difference quotients from calculus  • ## We have studied several types of functions whose limits can be evaluated by direct substitution. In this section, you will study several techniques for evaluating limits of functions for which direct substitution fails. Suppose you were asked to find the following limit. • ## Direct substitution fails because –3 is a zero of the denominator. By using a table, however, it appears that the limit of the function as x approaches –3 is –5. • ## Begin by factoring the numerator and dividing out any common factors. • ## = –5 • ## So, you can use g (x) to find the limit of f (x). • ## It is called an indeterminate form because you cannot, from the form alone, determine the limit. • ## After factoring and dividing out, you should try direct substitution again.  • ## f (x) = L2 or f (x)  L2 as x  c+ • ## From the graph of f, shown in Figure 11.15, you can see that f (x) = –2 for all x < 0. • ## = 2.   • ## A Limit from Calculus In the next section, you will study an important type of limit from calculus—the limit of a differencequotient. • ## Direct substitution produces an indeterminate form. • ## By factoring and dividing out, you obtain the following. • ## So, the limit is 6. Yüklə 0,64 Mb.

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