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Unformatted text preview: 5 Problem 4. [10 points] Estimate tan(0 . 001) using a linear approximation. 6 Problem 5. [10 points] Find the absolute minimum and the absolute maximum of the following function: f ( x ) = x 36 x 215 x + 25 for 0 ≤ x ≤ 6. 7 Problem 6. [20 points] Let f ( x ) = x 33 x 29 x + 6 . (a) [7 points] Find where f is increasing and where f is decreasing. (b) [7 points] Find where f is concave upward and where f is concave downward. Find the infection point(s). (c) [6 points] Using the in±ormation ±rom parts (a) and (b), sketch the graph o± f . 8 Problem 7. [10 points] Show that x > sin x for 0 < x < π/ 2. 9 Problem 8. [10 points] Find the limit. (a) [5 points] lim x → ln(1 + x ) tan x (b) [5 points] lim x →∞ x 1 x 10...
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 Fall '08
 MING
 Calculus, Derivative, Mathematical analysis, Convex function

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