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131f09x1-page2 - x equals 0 or 3(e f x is continuous for...

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Multiple choice. Circle the correct answer. (5 points each). 1. A function f ( x )iscont inuouseverywhere .Itsat isFes f (1) = 10 ,f (2) = 3 ,f (3) = - 5 , and f (4) = - 18 . The intermediate value theorem says that the equation (a) f ( x )=8 . 675309 has a solution for some x between 1 and 2. (b) f ( x )=8 . 675309 has a solution for some x between 2 and 3. (c) f ( x )=8 . 675309 has a solution for some x between 3 and 4. (d) f ( x )=8 . 675309 has a solution for some x with x< - 18. (e) It cannot be determined from the information whether f ( x )=8 . 675309 has a solution. 2. Let f ( x )= 8 > < > : x 2 +1 x - 1 if x< 0 2 x - 1i f0 x 3 p x +1 if x> 3 Then (a) f ( x )iscont inuousfora l lrea lnumbers . (b) f ( x )iscont inuousfora l lrea lnumbersexceptwhen x =0 . (c)
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Unformatted text preview: x equals 0 or 3. (e) f ( x ) is continuous for all real numbers except when x equals 0 , 1 or 3. 3. The squeeze theorem can be used to show that lim x ! x cos ✓ 1 x ◆ = 0 . To do so, you would need to use which of the following facts: (a) That 0 x cos ⇣ 1 x ⌘ x 2 for all real numbers x 6 = 0. (b) That-x 2 x cos ⇣ 1 x ⌘ x 2 for all real numbers x 6 = 0. (c) That 0 x cos ⇣ 1 x ⌘ x for all real numbers x 6 = 0. (d) That-x x cos ⇣ 1 x ⌘ x for all real numbers x 6 = 0. (e) That-| x | x cos ⇣ 1 x ⌘ | x | for all real numbers x 6 = 0. 2...
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