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Unformatted text preview: (0 , 0) and (2 , 8). (i). Explain without calculations why such point c necessarily exists. (ii). Find c . 1.5. Prove using the Mean Value Theorem: x 1 + x < ln(1 + x ) , for x > 0. 1.6. Prove using the Mean Value Theorem: e x > 1 + x + x 2 2 , for x > 0. 1.7. Show that the equation x 4 + 4 x + c = 0 has at most two real roots. Here c is an arbitrary constant. (Hint: argue by contradiction - suppose that there are three dierent roots. Now try to use Rolles theorem.) [This is Problem 20 in Section 4.2 of the textbook (p. 286).] 1...
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- Winter '10