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Unformatted text preview: information about the way (shown above) that the curve y = f ( x ) becomes unbounded as x . To determine such an asymptote, we rewrite the function f ( x ) = 4 x 2-3 2 x + 1 using long division: 2 x-1 2 x + 1 ) 4 x 2 + 0 x-3 4 x 2 + 2 x-2 x-3-2 x-1-2 Thus, f ( x ) = 4 x 2-3 2 x + 1 = 2 x-1-2 2 x + 1 , where lim x 2 2 x + 1 = 0 , and lim x - 2 2 x + 1 = 0 . So as x , the part of y = f ( x ) that does not go to zero is the line y = 2 x-1 . It follows that the curve y = f ( x ) approaches this (non-horizontal) line as x , or that the line y = 2 x-1 is an oblique asymptote for the curve. 2...
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