20b_04f_qe

20b_04f_qe - 20B Quizzes 12 points each Fall 2004 Bender...

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Unformatted text preview: 20B Quizzes 12 points each Fall 2004 Bender YOU MUST SHOW YOUR WORK. Q1. Evaluate the following. (a) d dx integraldisplay x 2 1 radicalbig t 3 + 1 dt (b) integraldisplay t √ t- 1 dt Q2. Consider the region R bounded by the parabola y = x (4- x ) = 4 x- x 2 and the line y = x for 0 ≤ x ≤ 3. (a) Find the area of the region R . (b) That part of the region R lying below y = 3 is rotated about the y-axis. Write down, but do not evaluate, an integral for the volume of the resulting region. Q3. (a) Write out the form of the partial fraction decomposition, but do NOT determine the numerical values of the coefficients: 5 ( x 2- 1) 2 ( x 2 + 1) . (b) Evaluate integraldisplay dx x 2 √ x 2- 1 . (c) Evaluate integraldisplay dx e x + 1 . Q4. (a) Write down the 3-interval Trapezoidal Rule approximation ( T 3 ) to integraltext 1 √ 1- x 3 dx . Don’t do any simplification. (b) Is the integral integraldisplay ∞ 4 dx ( x- 1) 2 convergent or divergent and why?...
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20b_04f_qe - 20B Quizzes 12 points each Fall 2004 Bender...

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