This preview shows page 1. Sign up to view the full content.
Unformatted text preview: handa (nh5757) – Areas using Riemann sums – bormashenko – (54880)
This printout should have 11 questions.
Multiplechoice questions may continue on
the next column or page – ﬁnd all choices
before answering. 1 42 3. S = k
k=1
7 001 10.0 points Evaluate k=1 4 n=2 1. 6k 4. S = n+1
.
n−1 42 5. S = 18
5 7
k=1
6 6. S = 2. 5 7
k=1 3. 20
3 004 4. 4 10.0 points Estimate the area under the graph of 5. None of these
002 f (x) = 4 sin x
10.0 points 15 (5 − 2k ). between x = 0 and x = π using ﬁve approx3
imating rectangles of equal widths and right
endpoints. k=12 Evaluate the given sum. 1. area ≈ 2.375 1. −80 2. area ≈ 2.355 2. −84 3. area ≈ 2.415 3. None of these 4. area ≈ 2.395 4. −92 5. area ≈ 2.335
005 5. −88
003 10.0 points Rewrite the sum Rewrite the sum
4+ S = 6 + 12 + 18 + . . . + 42
using sigma notation. 1
9 2 + 8+ 6 7k i
9 2 4i + i=1 7 i
9 2 4i + 1. k=1 9 2. S = 6
k=1 2
9 using sigma notation. 6 1. S = 10.0 points 2.
i=1 2 + . . . + 24+ 6
9 2 handa (nh5757) – Areas using Riemann sums – bormashenko – (54880)
9 4 i+ 3.
i=1
9 4 i+ 4.
i=1
6 5.
i=1 4 i+
i=1 006 i
9 6. 52 ft < distance < 69 ft 2 7. 52 ft < distance < 65 ft 4i
9 4i
i+
9 6 6. i
9 2 2 8. 54 ft < distance < 65 ft
9. 50 ft < distance < 67 ft 2 007 10.0 points Estimate the area under the graph of 2 f (x) = 18 − x2
10.0 points Cyclist Joe brakes as he approaches a stop
sign. His velocity graph over a 5 second period
(in units of feet/sec) is shown in on [0, 4] by dividing [0, 4] into four equal
subintervals and using right endpoints as sample points.
1. area ≈ 45 20 2. area ≈ 41 16 3. area ≈ 43
4. area ≈ 44 12 5. area ≈ 42
8 008 10.0 points Estimate the area, A, under the graph of 4 f ( x) =
1 2 3 4 5 Compute best possible upper and lower estimates for the distance he travels over this
period by dividing [0, 5] into 5 equal subintervals and using endpoint sample points.
1. 50 ft < distance < 65 ft on [1, 5] by dividing [1, 5] into four equal
subintervals and using right endpoints.
1. A ≈
2. A ≈ 2. 50 ft < distance < 69 ft 3. A ≈ 3. 54 ft < distance < 67 ft 4. A ≈ 4. 54 ft < distance < 69 ft 5. A ≈ 5. 52 ft < distance < 67 ft 5
x 20
3
77
12
79
12
19
3
13
2
009 10.0 points handa (nh5757) – Areas using Riemann sums – bormashenko – (54880)
Estimate the area, A, under the graph of n 4
f ( x) =
x 1. on [1, 5] by dividing [1, 5] into four equal
subintervals and using right endpoints. 2. i=1
n i=1
n 010 10.0 points 3.
i=1 The graph of a function f on the interval
[0, 10] is shown in n 4.
i=1 9
8
7
6
5
4
3
2
1 n 5. 8 i=1
n 6 6.
i=1 4
2 0
1 2 4 6 8 10 Estimate the area under the graph of f by
dividing [0, 10] into 10 equal subintervals and
using right endpoints as sample points.
1. area ≈ 52
2. area ≈ 54
3. area ≈ 51
4. area ≈ 55
5. area ≈ 53
011 10.0 points Rewrite the sum
4
2
5+
n
n 2 + 4
4
5+
n
n
+...+ using sigma notation. 2 4
2n
5+
n
n 2 4
2i
5i +
n
n
4
2i
5+
n
n
2i
4i
5+
n
n
2
4i
5+
n
n 2 2 2 2 2
4i
5i +
n
n 2 2i
4i
5+
n
n 2 3 ...
View
Full
Document
This note was uploaded on 11/21/2011 for the course M 408N taught by Professor Gualdini during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Gualdini
 Riemann Sums

Click to edit the document details