Mock Gateway 1 Answers - calculation lim x →-∞ 1 x 1...

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Answers to Mock Gateway I (Limits) 1. (a) about 2.5 (b) about 2.7 (c) -1 (d) -3 (e) DNE 2. 1,2 3. (a) lim x 3 ( x 2 - x + 2) = 3 2 - 3 + 2 = 8 (b) lim x 2 x 2 - 4 x - 2 = 0 0 So we need to do something: lim x 2 x 2 - 4 x - 2 = lim x 2 ( x - 2)( x + 2) x - 2 = lim x 2 x + 2 = 4 (c) If y is close to 2 and less than 2, then y - 2 is a small negative number: 3 y - 2 = 3 small negative number = big negative number So the answer is -∞ (d) + (e) Look at what happens when s 5 - and s 5 + . Either way, we have 5 small positive number = big positive number So the answer is + .

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(f) 5 3 4. (a) Everywhere. (b) Everywhere except where x = ± 5. 5. The answer to this should be obvious by staring at it. If it’s not, then here’s the
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Unformatted text preview: calculation: lim x →-∞ 1 ( x + 1) 2-2 = lim x →-∞ 1 x 2 + 2 x + 1-2 = lim x →-∞ 1 ( 1 x 2 ) ( x 2 + 2 x + 1) 1 x 2-2 = lim x →-∞ 1 x 2 1 + 2 x + 1 x 2-2 = 1 + 0 + 0-2 =-2 6. lim u →∞ 3 u 2 + 1 u 2 + 3 = lim u →∞ (3 u 2 + 1) 1 u 2 ( u 2 + 3) 1 u 2 = lim u →∞ 3 + 1 u 2 1 + 3 u 2 = 3 + 0 1 + 0 = 3 7. The vertical asymptote occurs where the denominator is zero and the horizontal asymptote occurs where lim x →∞ 3 x +1 2-x . Vertical: x = 2 Horizontal: y =-3...
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Mock Gateway 1 Answers - calculation lim x →-∞ 1 x 1...

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