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midterm2-pink-corr

midterm2-pink-corr - 16B CALCULUS Francisco Santos Midterm...

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Unformatted text preview: 16B CALCULUS Francisco Santos Nov 16, 2007 Midterm 2, (odd numbered seats) Name: 2 Emot‘f‘ca gal"? HIM 1. ( 20 points) Evaluate the following five deﬁnite and indeﬁnite integrals. Simplify your answers. SHOW your work. You may use u-substitution, trig formulas, the simple power rule, the fundamental theorem of calculus, integration by parts, partial fraction decomposition, etc. Sim"; v~ c945 'Y Ma «K Mama aw a“ .. ..____‘.M,j (95 ‘vc' can “A Name: 2 c 3 41.4 “H?” dx = --—-——-—- .~~ C. f(7+sm:t) (4;, u: 79",ng 0/01 7: Colix'dx ......,__.._.—-__...._~—_. 0 35—9 _ -—-,~;-—;‘ ‘: * / “W. ’ .‘ ~"r/g ‘ IT/Z e. foyxCOS-TdW: gljxsiwxj '"/ sc'uxalz : [Aﬁcwxj «— (pix ,.:' ‘ "I’ ‘42 Q s: / ”ﬁ‘mizgx 4x ' - l... , _, * L [6/u:¢l/;< (7.: 9m x " (,3, 9+ (0 yJ/QE .. ,..._--.._._~._ Name: ID: 3 2. ( 8 points) Find the total area of the region bounded by the graphs of y = x —— 1 and y = (:1: - 1)3. Set up but DO NOT EVALUATE the integral(s). Name: ID: 4 3. (10 points) The outdoor temperature at time t hours is modelled by T(t) = 55-45 cos (1350 -— 3)). a. What is the temperature at ,_ . L 3pm and 9pm ( t = 15 and t = 21)? 5(27)'~55*‘/5 523:7? ‘67 L .5111 ‘11 b. At what rate is the temperature changingTT' when t =5 hours? z“) 7.9/5 sam<g (JV 3) 42 .5 455;? SL'W(£ (4,3)) C/ T /(9 5 ﬂ fiim '71::9 , ‘ ,LT}I»1 g: 7/53; ‘1 c. What is the AVERAGE temperature between t = 9 and t = 21 hours? Name: ID' 4. (12 points) Consider the enclosed region R bounded by the graphs of y = ex, y = 82, z = 0. Set up but DO NOT EVALUATE the integral(s) which give the VOLUME of the solid of revolution formed by revolving the region R around a. the x-axis ”“i ;.'i_ ““""'i'-_-j‘-"+ b. the y-axis ...
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