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Unformatted text preview: saliyev (is4663) Homework 2 knopf (55420) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. This assignment covers Sections 2.4, 2.5, 3.1, and 3.2. 001 10.0 points How close to 5 do we have to take x for the inequality 1 ( x + 5) 2 > 700 to hold? 1. within at least 0 . 037 correct 2. within at least 0 . 077 3. within at least . 003 4. within at least 0 . 017 5. within at least 0 . 057 Explanation: We have to find the largest value of so that  x + 5  < = 1 ( x + 5) 2 > 700 , or, in other words, so that  x + 5  < = ( x + 5) 2 < 1 700 . Thus x must satisfy the inequality  x + 5  < 1 700 = 0 . 037 . Consequently, x must be within at least 0 . 037 of 5 if the inequality 1 ( x + 5) 2 > 700 is to hold. 002 10.0 points Determine which of the following could be the graph of f near the origin when f ( x ) = x 2 7 x + 10 2 x , x negationslash = 2 , 4 , x = 2 . 1. 2. correct 3. saliyev (is4663) Homework 2 knopf (55420) 2 4. 5. 6. Explanation: Since x 2 7 x + 10 2 x = ( x 2)( x + 5) 2 x = 5 x , for x negationslash = 2, we see that f is linear on ( , 2) uniondisplay (2 , ) , while lim x 2 f ( x ) = 3 negationslash = f (2) . Thus the graph of f will be a straight line of slope 1, having a hole at x = 2. This eliminates four of the possible graphs. But the two remaining graphs are the same except that in one f (2) > lim x 2 f ( x ) , while in the other f (2) < lim x 2 f ( x ) . Consequently, must be the graph of f near the origin. 003 10.0 points Determine which (if any) of the following functions is not continuous at x = 7. 1. f ( x ) = braceleftBigg 1 x 7 x negationslash = 7 7 x = 7 correct 2. f ( x ) = 1  x 5  x 7 1 2 x < 7 3. f ( x ) = braceleftBigg 28 2 x 7 x negationslash = 7 4 x = 7 4. f ( x ) = 1 x 5 x 7 1 2 x < 7 5. all continuous at x = 7 6. f ( x ) = braceleftbigg  x 7  x negationslash = 7 x = 7 saliyev (is4663) Homework 2 knopf (55420) 3 Explanation: A function f will be continuous at x = 7 when f (7) exists and lim x 7 f ( x ) = f (7) . Now f (7) exists for all the functions defined above; in addition, inspection shows that all these functions have the property lim x 7 f ( x ) = f (7) except for f ( x ) = braceleftBigg 1 x 7 x negationslash = 7 7 x = 7 . Consequently, this function is the only one that is not continuous at x = 7. 004 10.0 points Find all values of x at which f ( x ) = 5 1 sin x fails to be continuous. 1. x = 2 n + 3 2 , all integers n 2. x = n + 2 , all integers n 3. x = n + 4 , all integers n 4. x = n + 3 4 , all integers n 5. x = n, all integers n 6. x = 2 n + 2 , all integers n correct 7. x = 2 n, all integers n 8. x = (2 n + 1) , all integers n Explanation: The only values of x...
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 Spring '06
 McAdam
 Calculus

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