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1124worksheet1

# 1124worksheet1 - x dx Your signature(5 Use geometry to...

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Polytechnic Institute of NYU MA 1124 Worksheet 1 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 12 2 12 3 12 4 20 5 12 6 10 7 10 8 12 Total 100

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Your signature: (1) The velocity v ( t ) in the table below is decreasing, 4 t 16. Using n=6 subdivi- sions to approximate the total distance traveled, find t 4 6 8 10 12 14 16 v ( t ) 104 92 85 78 69 65 54 (a) an upper estimate (b) an lower estimate
Your signature: (2) Find the difference between the upper and lower estimates of the distance traveled at velocity f ( t ) on the interval a t b for n subdivisions. (a) f ( t ) = 4 t + 7, a = 2, b = 6, n = 200 (b) f ( t ) = cos t , a = - π 4 , b = π 2 , n = 100

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Your signature: (3) Given the following figure: (a) Find Z 2 - 3 f ( x ) dx . (b) Find Z 4 - 3 f ( x ) dx . (c) Find the area of the shaded region.
Your signature: (4) Use the following figure to find the integrals. (a) Z 3 . 5 . 5 f ( x ) dx (b) Z 4 . 5 . 5 f ( x ) dx (c) Z 4 . 5 2 f ( x ) dx (d) Z . 5 3 . 5 f ( x ) dx (e) Z 2

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Unformatted text preview: x ) dx Your signature: (5) Use geometry to ﬁnd the exact value of the following integrals. (a) Z 4 1 | x-2 | dx (b) Z 5 √ 25-x 2 dx Your signature: (6) Use geometry to ﬁnd the exact value of Z 6-6 | x-1 | dx + Z 6-6 √ 36-x 2 dx Your signature: (7) Given f ( x ) = √ 49-x 2 ﬁnd the average value of f ( x ) over the interval 0 ≤ x ≤ 7. Your signature: (8) For the function f below, consider the average value of f over the following intervals: I. ≤ x ≤ 1 II. ≤ x ≤ 2 II. 0 ≤ x ≤ 5 IV.-2 ≤ x ≤ 2 (a) For which interval is the average value of f least? (b) For which interval is the average value of f greatest? (c) For which pair of intervals are the average values equal?...
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