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Unformatted text preview: MAC 2311 Feb 8, 2006 Exam I and Key Prof. S. Hudson Show all your work and reasoning for maximum credit. If you continue your work on another page, be sure to leave a note. Do not use a calculator, book, or any personal paper. You may ask for extra paper; but please return it with your exam. 1) [20pt] Short answer problems. You may answer with ‘+ ∞ ’ or ‘∞ ’ but not with ‘d.n.e’. a) Solve for x, given that 1 2 x < 1. b) lim x → 1 x 1 √ x 1 = c) lim y → 6 + y +6 y 2 36 = d) lim x → + ∞ e x + e x e x e x = 2) [20pt] Same instructions as problem 1. a) lim x → tan(5 x ) sin(3 x ) cos(2 x ) = b) lim θ → sin 2 ( θ ) θ = c) lim x → + ∞ (1 + 1 2 x ) x = Hint: try a substitution. d) lim x → + ∞ 3 x 3 +2 x 2 + x x 3 +2 x 2 +3 x +4 = 3) (15pts) Answer True or False. You do not have to explain. a) tan( x ) is continuous on [ π/ 4 , π ]. b) cos( x ) ln( x ) is continuous on [ π/ 4 , π ]. c) lim x → sin( x 3 ) x 3 = 1. d) ∀ > 2 , ∃ δ > 3 , δ < . e) ∀ > 4 , ∃ δ > 3 , δ < . 4) [10pt] Sketch the curve by eliminating the parameter: x = √ t and y = 2 t + 1. 5) [10pt] Approximate the solution to x 3 + x 2 x +1 = 0 within 0.1, with some explanation of your reasoning. You can use the data below instead of a calculator (a little arithmetic and organization is left for you)....
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This note was uploaded on 05/28/2011 for the course MAC 2311 taught by Professor Staff during the Spring '08 term at FIU.
 Spring '08
 STAFF
 Calculus

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