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Unformatted text preview: x = 0 . a. (15 points) If y (0) =1 , compute y (0) . b. (5 points) Also compute y 00 (0) . 5 Problem 4 (20 points) Use diﬀerentials to ﬁnd an approximation to (26 . 96) 1 3 . Problem 5 A radioactive material of initial mass 20 milligrams decays to 5 milligrams after 5 years. a. 15 points Find an expression for the radioactive mass remaining after t years. 6 b. 5 points What is the halflife of the material? (Very ) Brief Solutions: 1a. f ( x ) =xe x cos(1e x )sin(1e x ) x 2 1b. y = ( x + 3) 10 ( x 29) 6 ( x1) 7 ± 10 x + 3 + 12 x x 29 + 7 x1 ² 1c. f ( x ) = arcsin( x ) + x √ 1x 2 1d. f (7) ( x ) =2 7 (7!) (2 x + 1) 8 2 dh dt  h =10 = 3 400 π ft ./ min . 3a. y (0) = 0 3b. y 00 (0) =2 / 3 4. 31 / 675 7 5a. m ( t ) = 20( 1 4 ) t/ 5 milligrams, or m ( t ) = 20 eln 4 5 t milligrams. 5b. 2.5 years 8...
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 Fall '08
 MING
 Math, Calculus, Cone, Radioactive Decay, HalfLife, Practice midterm exam

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