HW2 Solutions - ASSIGNMENT 2 - SOLUTIONS Problem 1. a) Both...

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Unformatted text preview: ASSIGNMENT 2 - SOLUTIONS Problem 1. a) Both F 1 ( x ) and F 2 ( x ) have x = 0 as the possible vertical asymptote. We check by computing one-sided limits: lim x + F 1 ( x ) = lim x + x 2 + 1 + 1 x = , lim x - F 1 ( x ) = lim x - x 2 + 1 + 1 x =- Either one of the above limits suffices to conclude that x = 0 is, indeed, a vertical asymptote for F 1 ( x ). But its a good idea to compute them both whenever possible, firstly because its good practice, and secondly because well have to do that latter on when well sketch graphs. Both lim x + F 2 ( x ) and lim x - F 2 ( x ) are of the form . If we use the conjugate, we get: x 2 + 1- 1 x = ( x 2 + 1- 1)( x 2 + 1 + 1) x ( x 2 + 1 + 1) = x 2 x ( x 2 + 1 + 1) = x x 2 + 1 + 1 ( x = 0) We now see that lim x + F 2 ( x ) = lim x + x 2 + 1- 1 x = lim x + x x 2 + 1 + 1 = 0 and, similarly, lim x - F 2 ( x ) = 0. Therefore x = 0 is not a vertical asymptote for...
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HW2 Solutions - ASSIGNMENT 2 - SOLUTIONS Problem 1. a) Both...

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