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Quiz 3 Solution - M 115 Quiz Three 10 points each(70...

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M 115 Quiz Three 10 points each (70 maximum) 1-3 Find the limit, if it exists. 1. lim x ± 3 x 2 ± 9 x ± 3 Solution: lim x ± 3 x 2 ± 9 x ± 3 ± lim x ± 3 ± x ± 3 ²± x ² 3 ² x ± 3 ± lim x ± 3 x ² 3 1 ± 6 ² ”b” a) 3 b) 6 c) 0 d) does not exist 2. lim x ± ² x 2 ± 2 x ² 1 3 x 3 ± 7 Solution: lim x ± ² x 2 ± 2 x ² 1 3 x 3 ± 7 ± lim x ± ² x 2 x 3 ± 2 x x 3 ² 1 x 3 3 ± 7 1 x 3 ± 0 ± 0 ² 0 3 ± 0 ± 0 ² ”c” a) 1 3 b) ± 1 7 c) 0 d) does not exist 3. lim x ± 4 x 2 ± 16 ± x ± 4 ² 3 Solution: lim x ± 4 x 2 ± 16 ± x ± 4 ² 3 ± lim x ± 4 ± x ± 4 ²± x ² 4 ² ± x ± 4 ² 3 ± lim x ± 4 x ² 4 ± x ± 4 ² 2 but 8 0 cannot exist, so ”d” a) 8 b) 4 c) 0 d) does not exist 1
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4-6: If f ± x ² ± 2 x , x ² 0 x 2 ,0 ± x ² 1 2 x ² 1, x ± 1 ± 2 1 2 x 2 , x ³ 2 4. At x ± 0, f is: a) continuous but not differentiable. b) continuous and differentiable c) differentiable but not continuous d) neither continuous nor differentiable.
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