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Answers to even-numbered HW - Test 2

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Answers to Even-Numbered HW - Test 2 HW #7 - 13 HW 7 p. 96 2. lim x 1 - f ( x ) = 3 means we can make f ( x ) as close to 3 as we like by taking x sufficiently close to 1 from the left, but not equal to 1. lim x 1+ f ( x ) = 7 means we can make f ( x ) as close to 7 as we like by taking x sufficiently close to 1 from the right, but not equal to 1. The (two-sided) limit lim x 1 f ( x ) does not exist (DNE) since the left hand limit is not equal to the right-hand limit. 4. (a) 2; (b) 4; (c) 2; (d) DNE; (3) 3. 6. (a) 4; (b) 4; (c) 4; (d) undefined; (e) 1; (f) -1; (g) DNE; (h) 1; (i) 2; (j) undefined; (k) 3; (l) DNE; this is because we can’t make f ( x ) as close as we like to some number L by taking x sufficiently close to 5 from the left, but not equal to 5. A reasonable guess for L would be 4, but if we want f ( x ) within 0.5 of 4, you can see no matter how close we make x to 5 from the left, some values of f ( x ) will always overshoot the range (3 . 5 , 4 . 5). 8. (a) -∞ ; (b) ; (c) -∞ ; (d) ; (e) x = - 3; x = 2; x = 5. 14. There are many correct answers. Just draw little sections of the graph with each one satisfying a stated condition. You don’t even have to connect up the different sections, although that would give a more typical-looking function. 26. To see that this is an infinite limit, just substitute - 3 in the numerator and denominator: - 1 0 is infinite. To get the right sign, substitute a value of x slightly to the left of - 3. The denominator will be negative, and the numerator will be close to - 1. The two negatives give (positive) .

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