finA05fk - MAC 2311 Final Exam A[recent topics and Key Prof...

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MAC 2311 Dec 12, 2005 Final Exam A [recent topics] and Key Prof. S. Hudson 1) (20 pts) Compute and simplify; x 7 + e x dx = sec( x ) tan( x ) dx = 2 x x 2 +1 dx = 1 - 2 t 3 t 3 dt = 2) (15 pts) More: e 5 x dx = cos 2 ( x ) dx = tan 2 ( x ) dx = 3) (15 pts) A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (I drew a picture on the board - imagine a rectangle divided down the middle by a vertical line). What dimensions should be used so that the enclosed area will be a maximum? [If you don’t understand this story, ask me!] 4) (15 pts) Sketch a graph of y = x 2 - 1 x 3 . Find all critical points, inflection points and asymptotes [and label them clearly]. You may use: y = 3 - x 2 x 4 y = 2( x 2 - 6) x 5 3 1 . 8 6 2 . 4 1 . 8 - 3 0 . 18 2 . 4 - 3 0 . 07 5) (10 pts) CHOOSE ONE; A) State and prove Rolle’s thm. B) Prove that if f ( x ) > 0 on [a,b] then f is increasing on [a,b]. C) Prove the substitution rule of ch 6.3. 1
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6) (15 pts) Answer TRUE or FALSE: A continuous function defined on ( -∞ , + ) must have a minimum value.
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