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Unformatted text preview: + b if x ≥ 2. Find the values of a and b so that f has a continuous derivative on all of R . 5. Verify that ( tan-1 ( x )) = 1 / (1 + x 2 ). 6. Page 202 - 208 # 9, 14, 36, 36, 40. 7. Let f ( x ) = sin ( x )-2 x + 1 . Find the exact number of roots of f and fully justify your ﬁndings. 8. Let g ( x ) = xe 2 x . Find a formula for g ( n ) ( x ) for a natural number n and then verify your claim with a good proof using the PMI. 9. Let a,b > 0 be constants and let h ( x ) = x a (1-x ) b where x ∈ [0 , 1]. Use the EVT to justify that h has an absolute max on [0 , 1] and then ﬁnd this value and where it occurs. 10. Prove that tan ( x ) > x for all x ∈ (0 , π 2 ). NOTE: Reading Week is Monday, July 2 to Friday, July 6, so there are no classes that week. MATA37 will resume on Tuesday, July 10....
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This note was uploaded on 10/28/2010 for the course MATHEMATIC MATA37 taught by Professor Vadim during the Winter '08 term at University of Toronto.
- Winter '08