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141Bquiz1c - t is the time measured in hours Use...

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1 MATH 141B QUIZ#1 Due: Tues Jan 22, 2008 Instructor: Dr. Fabbri Duration: 15 minutes [ 2 ] 1. Compute the definite integral integraldisplay π 0 x 2 cos x dx and circle the correct answer below. A) - 2 π , B) π , C) - π, D) 2 π E) none of the above [ 2 ] 2. If f ( x ) = x 5 ln x and f (1) = - 1 16 then find f ( 1 2 ) . [Method: Integrate f (using parts) and add C to get f . Use the initial condition to find the value of C, and finally evaluate f ( x ) at x = 1 2 . ] A) 0, B) 4 ln 2 - 1, C) ln(1 / 2) - 1 16 , D) ln 2 E) none of the above
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2 [ 2 ] 3. Suppose that an oral dose of a drug is taken. From that time, the drug is assimilated in the body and excreted through the urine. The total amount of drug that has passed though the body in time T is given by integraldisplay T 0 E ( t ) dt where E is the rate of excretion of the drug. A typical rate-of-excretion function is E ( t ) = te kt , where k > 0 and
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Unformatted text preview: t is the time measured in hours. Use integration by parts to ±nd a formula for I T E ( t ) dt . A) 1 k 2 (1-e − kT ) B) 1 k 2 (1-ke − kT ), C) 1 k 2 ( T-ke − kT + 1) D) 1 k 2 [1-e − kT ( kT + 1)] E) none listed [ 2 ] 4. Determine whether the improper integral i ∞ 3 1 + x dx is convergent or divergent, and circle the correct answer below. A) conv. to 0, B) conv. to 1, C) div to + ∞ , D) div to-∞ , E) none listed 3 [ 2 ] 5. Determine whether the improper integral i ∞ sin √ x √ x dx is convergent or divergent, and circle the correct answer below. A) conv. to -2, B) conv. to 1, C) div to + ∞ , D) div to-∞ , E) none listed...
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