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Unformatted text preview: km/h. Explain why the police have a right to charge you with a speeding violation. 3. Use the Mean Value Theorem to prove the inequality | cos a-cos b | | a-b | for all real numbers a and b. (Hint: See Exercise #29 in Section 4.2 of the textbook.) 4. Prove the following statements: (a) The equation x 3 + 4 x-1 = 0 has exactly one real root. (b) If b 2-3 ac < and a 6 = 0 , then the equation ax 3 + bx 2 + cx + d = 0 has exactly one real root. (Hint: We already know that every cubic polynomial has at least one real root from Assignment 4, Part 2.) 1 5. Show that e x > 1 + x + x 2 2 for all x > . (Hint: Let f ( x ) = e x-(1 + x + x 2 / 2) . What is f (0) ? What can you say about the sign of f ( x ) ?) 2...
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- Spring '10