Explanation Given information: The function, R ( x ) = x 3 − 2 x 2 + 4 x − 8 x 2 − 11 x + 18 . Explanation: Let, R ( x ) = x 3 − 2 x 2 + 4 x − 8 x 2 − 11 x + 18 . By factoring, ⇒ R ( x ) = x 3 ( x − 2 ) + 4 ( x − 2 ) x 2 − 2 x − 9 x + 18 ⇒ R ( x ) = x 2 ( x − 2 ) + 4 ( x − 2 ) x ( x − 2 ) − 9 ( x − 2 ) ⇒ R ( x ) = ( x 2 + 4 ) ( x − 2 ) ( x − 2 ) ( x − 9 ) ⇒ R ( x ) = ( x 2 + 4 ) ( x − 2 ) ( x − 2 ) ( x − 9 ) The given function is a rational function. Rational function is undefined where denominator is zero. Hence R ( x ) is undefined at ( x − 2 ) ( x − 9 ) = 0 . That is R ( x ) is undefined at x = 2 and x = 9 . The vertical asymptote occurs where denominator of function is zero but numerator at that point is not zero

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Chapter 13, Problem 29RE

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The values where the rational function R(x)=x3−2x2+4x−8x2−11x+18 is undefined and then determine an asymptote or a hole appears at such numbers.

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Chapter 13, Problem 28RE

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Chapter 13 Solutions

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Ch. 13.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 13.1 - If f( x )={ xifx0 1ifx0 what is f( 0 ) ?...Ch. 13.1 - 3. The limit of a function f (x) as x approaches c...Ch. 13.1 - If a function f has no limit as x approaches c,...Ch. 13.1 - True or False may be described by saving that the...Ch. 13.1 - True or False lim xc f( x ) exists and equals some...Ch. 13.1 - Ch. 13.1 - lim x3 ( 2 x 2 +1 )Ch. 13.1 - Ch. 13.1 - lim x0 2x x 2 +4

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The values where the rational function R ( x ) = x 3 − 2 x 2 + 4 x − 8 x 2 − 11 x + 18 is undefined and then determine an asymptote or a hole appears at such numbers.

Solution Summary: The author explains that the rational function R(x) is undefined and determines an asymptote or hole at such numbers.

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The values where the rational function R(x)=x3−2x2+4x−8x2−11x+18 is undefined and then determine an asymptote or a hole appears at such numbers.

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Chapter 13 Solutions