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review - (b Which is larger RIGHT(4 of LEFT(4 How do you...

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Name: PID: Sec. No: Sec. Time: Math 10B Review Assignment September 2, 2010 Please turn in on Thursday in class. This assignment may replace your worst homework. Show all of your work, no credit will be given for unsupported answers. Please write neatly and make sure the answer is clear. 1. Please compute the following indefinite integrals. (a) x ( x + 4)( x - 3) dx (b) x + 1 x - 4 dx (c) x ln(3 x ) dx

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2. Find the volume of the figure formed by revolving the region between the functions f ( x ) = x and h ( x ) = x on [0 , 1] around the line y = 3. 3. Solve the following initial value problem ds dt = s 2 sin( t ) s ( π ) = 1 4. Consider the function g ( x ) = x 3 + x - 1 on [0 , 4]. Please answer the following questions. (a) Which is larger, TRAP(4) of MID(4)? How do you know? Compute the larger of the two.

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Unformatted text preview: (b) Which is larger, RIGHT(4) of LEFT(4)? How do you know? Compute the larger of the two. 5. Consider the function deﬁned by G ( y ) = Z y 2 4 x 1 + x 2 dx (a) Compute G (5). (b) Compute G (5). (c) Find the absolute minimum of G ( x ) on [5 , ∞ ). Explain your reasoning. 6. Find the volume of the 3D object whose base lies between the function y = x 2 and the y-axis from y = 0 to y = 3 and whose cross sections perpendicular to the y-axis are equilateral triangles. 7. Determine whether the following improper integral converges or diverges. You do not need to ﬁnd the value if it does converge. Z ∞ 4 1 x 2-2 dx...
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