spring 06 final

# Thomas' Calculus: Early Transcendentals

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Mathematics 104 Spring Term 2006 Final Examination May 18, 2006 1. Evaluate Z x 2 (1 + x 2 ) 3 / 2 dx . 2. Evaluate Z ln( x 2 + 2 x + 2) ( x + 1) 2 dx . 3. Does Z 2 ln( e x - 2) x 3 + 1 dx converge or diverge? Give your reasons. 4. (a) Does X n =0 3 n ( n !) 2 (2 n )! converge or diverge? Give your reasons. (b) Does X n =1 e 10 n + n 10 n n converge or diverge? Give your reasons. 5. For what values of x does X n =2 x n n (ln n ) 1 2 converge? Give your reasons. 6. Find lim x 0 e 2 x - cos x - sin 2 x ln(1 + x ) - x . Show your work. 7. Write (1 + i ) 15 (1 + i 3) 17 in polar form re with r 0 and 0 θ < 2 π . 8. Find all real solutions to the diﬀerential equation cos
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Unformatted text preview: 2 x dy dx + y = e tan x . Show your work. 9. Find all real solutions to the diﬀerential equation d 2 y dx 2 + dy dx-2 y = e 3 x . Show your work. 10. Find the volume of the solid obtained by revolving the region under the curve y = cos x and above the x-axis, for 0 ≤ x ≤ π/ 3, about the line x =-1. Show your work. 11. Find the length of the curve given in parametric form by ± x = 2( t 2-1) 3 / 2 y = 3 t 2 where 2 ≤ t ≤ 3....
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