t-cl-selo.2011t - . g Compute the sum of this geometric...

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Sets and Logic MHF32022787 Prereq-T Prof. JLF King 25Aug2011 T1: Show no work. NOTE : The inverse-fnc of g , often written as g 1 , is different from the reciprocal fnc 1 /g . E.g, suppose g is invertible with g ( 2) = 3 and g (3) = 8: Then g 1 (3) = 2, yet [1 /g ](3) def === 1 /g (3) = 1 / 8. Please write DNE in a blank if the described object does not exist or if the indicated operation cannot be performed. a ± 2 27 ² 3 = ........... . log 8 (4)= ........... . b Line y = [ M · x ] + B owns points (3 , 1) and ( 3 , 17). Hence M = ............... and B = ............... . c Quadratic 15 x 2 + 23 x + 6 = [ Ax - α ] · [ Bx - β ], for numbers A = ..... , α = ..... ; B = ..... , β = ..... . d Below, f and g are differentiable fncs with f (2) = 3 , f 0 (2) = 19 , f (3) = 5 , f 0 (3) = 17 , g (2) = 11 , g 0 (2) = 1 2 , g (3) = 13 , g 0 (3) = 7 , g (5) = 23 , g 0 (5) = 29 . Define the composition C := g f . Then C (2) = ....... ; C 0 (2) = ........................... . Please write each answer as a product of numbers; do not multiply out. [ Hint: The Chain rule. ] e Let y = f ( x ) := ± 7 + 3 2 x ²³ 5. Its inverse-function is f 1 ( y )= ........................................... . f Let g ( x ) := x 3 + x . Then g 1 (10)= ............... and [ g 1 ] 0 (10)= ....................................
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Unformatted text preview: . g Compute the sum of this geometric series: ∞ X k =5 [ 1] k · [1 / 3] 2 k = .................................... . h ∞ X n =1 r n = 2011. So r = ................ or DNE . [ Hint: The sum starts with n at one , not zero. ] T2: Math-Greek alphabet : Please write the two miss-ing data of lowercase/uppercase/name. Eg: “iota: .. α : .... B: .... .” You fill in: ι I A alpha β beta . Γ: ............ Δ: ............ Υ: ............ ν : ............ ζ : ............ μ : ............ sigma ...... xi ...... omega ...... lambda ...... End of Prereq-T T1: 160pts T2: 20pts Total: 180pts Please PRINT your Name .................................................. Honor Code: “I have neither requested nor received help on this exam other than from my professor.” Signature: .............................................
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This note was uploaded on 01/26/2012 for the course MHF 3202 taught by Professor Larson during the Fall '09 term at University of Florida.

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