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Chapter 4 | Applications of Derivatives
Figure 4.54 The graph of this rational function approaches the horizontal asymptote y =0 as x →±∞.
c. Dividing the numerator and denominator by x , we have lim x →±∞ 3 x 2 +4 x x +2 = lim x →±∞ 3 x +4 1+2/ x . As x →±∞, the denominator approaches 1. As x →∞, the numerator approaches +∞. As x →−∞, the numerator approaches −∞. Therefore lim x →∞ f ( x ) =∞, whereas lim x →−∞ f ( x ) =−∞ as shown in the following figure.
Figure 4.55 As x →∞, the values f ( x )→∞. As x →−∞, the values f ( x )→−∞.
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