exam2sol_v2

exam2sol_v2 - Name: _ PID: _ TA: _ Sec. No: _ Sec. Time: _...

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1. (a) (3 points) Find LEFT(2) and RIGHT(2) for 4 2 0 (1 ) x dx + . Notice that D x = ( b a )/ n = (4 – 0)/2 = 2. We begin by creating a table of values which will help us compute the quantities LEFT(2) and RIGHT(2). 02 4 () 1 5 1 7 x fx LEFT(2) = D x [ f (0) + f (2)] = 2[1 + 5] = 12. RIGHT(2) = D x [ f (2) + f (4)] = 2[5 + 17] = 44. (b) (2 points) For each approximation: is it an underestimate or an overestimate? Explain your answers. On the interval [0, 4], x 2 + 1 is increasing, so we have that LEFT(2) is an underestimate RIGHT(2) is an overestimate. (c) (3 points) Find MID(2) and TRAP(2) for 4 2 0 ) x dx + . Again, we use the same D x , as in part (a). We need a slightly larger table to compute MID(2). Recall, though, that TRAP(2) = [LEFT(2) + RIGHT(2)]/2.
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This note was uploaded on 04/02/2010 for the course MATH 10b taught by Professor Lender during the Spring '08 term at UCSD.

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exam2sol_v2 - Name: _ PID: _ TA: _ Sec. No: _ Sec. Time: _...

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