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(Solved) Donnie Smith Assignment Section 6.5 due 04/13/2017 at 11:59pm MST 1. (1 point) Given the following integral and value of n, approximate the following...


Hi can you please help me with problem 3, I understand but I don't know what I am doing wrong. please explain to me how to do the problem using left right midpoint trapezoid and Simpson's rule

Donnie Smith
Assignment Section 6.5 due 04/13/2017 at 11:59pm MST 1. (1 point) Given the following integral and value of n,
approximate the following integral using the methods indicated
(round your answers to six decimal places):
Z 1 Sharma MAT 266 ONLINE B Spring 2017  2 e−5x dx, n = 4 = Midpoint =  0 (a) Trapezoidal Rule (b) Midpoint Rule  = Trapezoid =
Simpson’s = (c) Simpson’s Rule Answer(s) submitted:
Answer(s) submitted:
• 0.3954
• 0.3959
• 0.3955 (correct)
2. (1 point) A radar gun was used to record the speed of
a runner during the first 5 seconds of a race (see table). Use
Simpson’s rule to estimate the distance the runner covered during those 5 seconds. t(s)
v(m/s) 0
0 0.5
2.4 1
3.3 1.5
6.2 2
6.75 2.5
8.55 3
9.45 3.5
10.15 4
10.45 Answer(s) submitted:
• 37.141 (correct)
3. (1 point) Estimate

Left = R 4.75 −1.5 |2 − x| dx using 5 divisions and •
•
•
•
•
•
•
•
•
•
•
•
•
•
4.5 •
10.75•
•
•
•
•
•
•
• 1.25
1
2.25
3.5
4.75
6
21.875
1.25
2.25
3.5
4.75
6
7.25
29.6875
5
1.25
10.75
1.125
1.75 (score 0.217391304347826)
4. (1 point)
R
x
Consider the integral approximation T20 of 05 2e− 4 dx.
Does T20 overestimate or underestimate the exact value?  • A. overestimates
• B. underestimates = Right = Find the error bound for T20 without calculating TN using the
result that
M(b − a)3
Error(TN ) ≤
,
12N 2  1 where M is the least upper bound for all absolute values of the
x
second derivatives of the function 2e− 4 on the interval [a, b].
Error(T20 ) ≤
Answer(s) submitted:
• A
• 0.003255 (correct)
1. Take the sample points from the left-endpoints.
Answer: L4 =
2. Is your estimate L4 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
3. Take the sample points from the right-endpoints.
Answer: R4 =
4. Is your estimate R4 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
5. Use the Trapezoid Rule with n = 4.
Answer: T4 =
6. Is your estimate T4 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate 5. (1 point) Use six rectangles to find an estimate of each type
for the area under the given graph of f from x = 0 to x = 12. 1. Take the sample points from the left-endpoints.
Answer: L6 =
2. Is your estimate L6 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
3. Take the sample points from the right-endpoints.
Answer: R6 =
4. Is your estimate R6 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
5. Take the sample points from the midpoints.
Answer: M6 = Note: You can click on the graph to enlarge the image.
Answer(s) submitted:
• 20.8
• Underestimate
• 25.2
• Overestimate
• 23
• Overestimate (correct) Note: You can click on the graph to enlarge the image. 7. (1 point)
R
The graph of a function f is given below. Estimate 08 f (x) dx
using four subintervals with (a) right endpoints, (b) left endpoints, and (c) midpoints.
R
(a) 08 f (x) dx ≈
R
(b) 08 f (x) dx ≈
R
(c) 08 f (x) dx ≈ Answer(s) submitted:
•
•
•
•
• 47.78
Overestimate
39.78
Underestimate
44.12 (correct) 6. (1 point) Use four rectangles to find an estimate of each
type for the area under the given graph of f from x = 1 to x = 9.
2 0.8675, 0.8632, and 0.9540, and the same number of subintervals were used in each case. Answer(s) submitted:
• 4.2
• 6.2
• 10 (a) Which rule produced which estimate? (correct) ?
?
?
? 8. (1 point) Given the following graph of the function
y = f (x) and n = 6, answer the following questions about the
area under the curve from x = 0 to x = 6. of 1.
2.
3.
4. (b) Between which two approximations does the true value
0 f (x) dx lie? R2 •
•
•
• 1. Use the Trapezoidal Rule to estimate the area.
Answer: T6 =
2. Use Simpson’s Rule to estimate the area.
Answer: S6 = Right-hand estimate
Left-hand estimate
Midpoint Rule estimate
Trapezoidal Rule estimate A. 0.8632 < 02 f (x) dx < 0.8675
B. No conclusions
can be drawn.
R
C. 0.8675 < 02 f (x) dx < 0.9540
R
D. 0.7811 < 02 f (x) dx < 0.8632
R Answer(s) submitted:
•
•
•
•
• Note: You can click on the graph to enlarge the image. 7811
9540
8632
8675
A (correct) Answer(s) submitted: 11. (1 point) Consider the four functions shown below. On
R
the first two, an approximation for ab f (x) dx is shown. • 30.5
• 29.667 (incorrect)
9. (1 point)
Estimate the area under the graph in the figure by using (a)
the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s
Rule, each with n = 4. T4 ≈
M4 ≈
S4 ≈ 1. 2. 3. 4. Answer(s) submitted: (Click on any graph to get a larger version.)
1. For graph number 1, Which integration method is shown?
• A. trapezoid rule
• B. left rule
• C. right rule
• D. midpoint rule
Is this method an over- or underestimate?
• A. over • 11.5
• 12
• 11.66 (correct)
10. (1 point)
The left, right, Trapezoidal, and Midpoint Rule approximaR
tions were used to estimate 02 f (x) dx, where f is the function whose graph is shown below. The estimates were 0.7811,
3 • B. under
2. For graph number 2, Which integration method is shown?
• A. left rule
• B. trapezoid rule
• C. midpoint rule
• D. right rule
Is this method an over- or underestimate?
• A. under
• B. over
3. On a copy of graph number 3, sketch an estimate with
n = 2 subdivisions using the right rule.
Is this method an over- or underestimate?
• A. over
• B. under
4. On a copy of graph number 4, sketch an estimate with
n = 2 subdivisions using the trapezoid rule.
Is this method an over- or underestimate?
• A. under
• B. over • U
• B (correct)
13. (1 point) Use six rectangles to find an estimate of each
type for the area under the given graph of f from x = 0 to x = 12. 1. Take the sample points from the left-endpoints.
Answer: L6 =
2. Is your estimate L6 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
3. Take the sample points from the right-endpoints.
Answer: R6 =
4. Is your estimate R6 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
5. Take the sample points from the midpoints.
Answer: M6 = Answer(s) submitted:
• D
• A
• A
• A
• B
• B (correct)
12. (1 point)
R
Estimate 01 cos(x2 ) dx using (a) the Trapezoidal Rule and (b)
the Midpoint Rule, each with n = 4. Give each answer correct
to five decimal places.
(a) T4 =
(b) M4 = Note: You can click on the graph to enlarge the image.
Answer(s) submitted: (c) By looking at a sketch of the graph of the integrand, determine for each estimate whether it overestimates, underestimates, or is the exact area. •
•
•
•
• ? 1. M4
? 2. T4 (score 0.4000000059604645) (d) What can you conclude about the true value of the integral?
•
•
•
•
• 75.6
Overestimate
83.6
Underestimate
80.2 14. (1 point) Use six rectangles to find an estimate of each
type for the area under the given graph of f from x = 0 to x = 12. A. M4 < 01 cos(x2 ) dx < T4
R
B. T4 < 01 cos(x2 ) dx < M4
C. No conclusions
can be drawn.R
R
D. T4 < 01 cos(x2 ) dx and M4 < 01 cos(x2 ) dx
R
R
E. T4 > 01 cos(x2 ) dx and M4 > 01 cos(x2 ) dx
R Answer(s) submitted:
• 0.895759
• 0.908907
• O
4 1. Take the sample points from the left-endpoints.
Answer: L6 =
2. Is your estimate L6 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
3. Take the sample points from the right-endpoints.
Answer: R6 =
4. Is your estimate R6 an underestimate or overestimate of
the true area?
• Choose one
• Underestimate
• Overestimate
5. Take the sample points from the midpoints.
Answer: M6 = Answer(s) submitted:
•
•
•
•
• (incorrect)
15. (1 point) Determine whether the integral is divergent or
convergent. If it is convergent, evaluate it. If not, state your
answer as divergent .
Z ∞
0 Answer(s) submitted:
• 7 Note: You can click on the graph to enlarge the image. (correct)
c
Generated by WeBWorK,
http://webwork.maa.org, Mathematical Association of America 5 7e−x dx

 


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