# Test 2 Solution - MAT197 Calculus B Winter 2014 Solution of...

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MAT197 - Calculus B - Winter 2014 Solution of Term Test 2 - February 27, 2014 Time allotted: 90 minutes. Aids permitted: None. PART I No explanation is necessary. For questions 1–4, please fill in the blanks. (4 marks) 1. What is the best substitution to calculate Z 1 17 + 16 x + 4 x 2 dx ? 2. What are two good substitutions to calculate 2 dx ?
3. Using the Trapezoid Rule with n = 10 we obtain an error of 1 when computing the integral What is the smallest value for n to obtain an error of at most 10 - 6 ?
4. During Cinco de Mayo, you shoot a bullet straight up into the sky at the speed of 500 m/s. The altitude of the bullet y ( t ) at time t seconds after being shot satisfies the differential equation y 00 = - g . What is the velocity of the bullet when it hits the ground?
MAT197 – Solution of Term Test 2 For questions 5-8, please choose the correct answer. (4 marks) 5. Which terms appear in the partial fraction decomposition of ( x - 2) 2 ( x - 1) ( x + 1)( x 2 + 3) 2 ( x - π ) 2 ? (Select all that apply) (a) A x - 1 (b) B x - 2 (c) C ( x - 2) 2 (d) D x + 1 (e) E x - π (f) F ( x - π ) 2 (g) Gx + H x 2 + 3 (h) Ix + J ( x 2 + 3) 2 (i) Kx + L ( - 0 . 5 marks for each wrong)
6. Which of the following integrals is convergent?