prob5 - with respect to time r t t A B C D E Do the birds...

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Chapter 5 1. Section 5.1 1. The velocity v ( t ) in the table below is increasing. Use n = 4 subdivisions to approximate the total distance traveled. Also, ﬁnd t 3 6 9 12 15 f ( t ) 20 21 25 30 40 (a) An upper estimate. (b) A lower estimate. 2. Consider the function f ( x ) = 1 1 + x 2 for - 2 x 2 Use Δ x = 1 to ﬁnd the: (a) Left sum (b) Right sum 2. Section 5.2 1. Estimate the integral with n = 4 using the following techniques Z 6 2 1 + x 2 dx (a) Left-hand sum (b) Right-hand sum 2. For question 1 above, how far oﬀ can your estimates be from the true value? 3. Without computing anything, what is the value of Z 2 π 0 sin( x ) dx 4. Compute the following sum by interpreting it as a limit of Riemann sums. lim n →∞ (2 /n ) n - 1 X i =0 p 2 - (2 i/n ) 2 5. Evaluate the deﬁnite integral Z b a xdx by using the deﬁnition. Don’t use the fundamental theorem of calculus or geometry. 1

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3. Section 5.3 1. The follwing graph shows the rate at which a population of migratory birds enter and leave a swamp
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Unformatted text preview: with respect to time. r ( t ) t A B C D E Do the birds like the swamp? Mark the places when the population growth accelerates and deaccelerates? When does the population decline? 2. Using the ﬁgure below, list the following from least to greatest. (a) The average value of f ( x ) on 0 ≤ x ≤ 2. (b) The average of f (0) and f (2). (c) The average value of f ( x ) on 0 ≤ x ≤ 5. (d) Z 5 f ( x ) dx 1 2 3 4 5-2-1 1 f ( x ) 4. Section 5.4 1. Suppose we have R 10 2 f ( x ) dx = 2 and R 16 2 f ( x ) dx = 5. What is the value of R 16 10 f ( x ) dx . 2. Find the area between the functions f ( x ) = x 2-1 and g ( x ) = x between the points of intersection....
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

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prob5 - with respect to time r t t A B C D E Do the birds...

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