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Use Limits to Describe the Behavior of the Rational Function f(x)=x+1x2−2xf ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }

Question 168

Multiple Choice

Use limits to describe the behavior of the rational function near the indicated asymptote.
- f(x) =x+1x2−2xf ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }
Describe the behavior of the function near its vertical asymptotes.


A) lim⁡x→θ−f(x) =∞,lim⁡x→θ+f(x) =−∞,lim⁡x→2−f(x) =∞,lim⁡x→2+f(x) =−∞\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = - \infty
B) lim ⁡x→θ−f(x) =0,lim⁡x→θ+f(x) =−∞,lim⁡x→2−f(x) =−∞,lim⁡x→2+f(x) =∞\operatorname { lim~ } _ { x \rightarrow \theta ^ { - } } f ( x ) = 0 , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = - \infty , \quad \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty
C) lim⁡x→θ−f(x) =∞,lim⁡x→θ+f(x) =−∞,lim⁡x→2−f(x) =−∞,lim⁡x→2+f(x) =∞\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty
D) lim⁡x→θ−f(x) =−∞,lim⁡x→θ+f(x) =∞,lim⁡x→Z−f(x) =−∞,lim⁡x→2+f(x) =∞\lim _ { x \rightarrow \theta ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow \theta ^ { + } } f ( x ) = \infty , \lim _ { x \rightarrow \mathbb { Z } ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 2 ^ { + } } f ( x ) = \infty

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