Evaluate Representative Graph: *** To see FULL resolution of the image: Right cl

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Evaluate

Representative Graph:

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EXAMPLE 5 Evaluate 3x2- x - 2 lim SOLUTION As x becomes large, both numerator and denominator become large, so it isn't obvious what happens to their ratio. We need to do some preliminary algebra To evaluate the limit at infinity of any rational function, we first divide both numerator and denominator by the highest power of x that occurs in the denominator. (we may assume that x 0, since we are interested only in large values of X.) In this case the highest power of X is xz, and so, using the Limit Laws, we have 3x2 - x- 2 3x lim = lim 2 = lim 2 2 lim 3- lim lim 4+2 lim + lim - 3-0 [by this rule] A similar calculation shows that the limit as x -00 is also . The figure illustrates the results of these calculations by showing how the graph of the given rational function approaches the horizontal asymptote y -

Explanation / Answer

Solution:

The value is 3/4

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