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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 eâˆ’5x dx, n = 4 = Midpoint = 0 (a) Trapezoidal Rule (b) Midpoint Rule = Trapezoid =

Simpsonâ€™s = (c) Simpsonâ€™s Rule Answer(s) submitted:

Answer(s) submitted:

â€¢ 0.3954

â€¢ 0.3959

â€¢ 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

Simpsonâ€™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:

â€¢ 37.141 (correct)

3. (1 point) Estimate

Left = R 4.75 âˆ’1.5 |2 âˆ’ x| dx using 5 divisions and â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

4.5 â€¢

10.75â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢ 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 2eâˆ’ 4 dx.

Does T20 overestimate or underestimate the exact value? â€¢ A. overestimates

â€¢ B. underestimates = Right = Find the error bound for T20 without calculating TN using the

result that

M(b âˆ’ a)3

Error(TN ) â‰¤

,

12N 2 1 where M is the least upper bound for all absolute values of the

x

second derivatives of the function 2eâˆ’ 4 on the interval [a, b].

Error(T20 ) â‰¤

Answer(s) submitted:

â€¢ A

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ Overestimate

5. Use the Trapezoid Rule with n = 4.

Answer: T4 =

6. Is your estimate T4 an underestimate or overestimate of

the true area?

â€¢ Choose one

â€¢ Underestimate

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ 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:

â€¢ 20.8

â€¢ Underestimate

â€¢ 25.2

â€¢ Overestimate

â€¢ 23

â€¢ 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 â‰ˆ

R

(b) 08 f (x) dx â‰ˆ

R

(c) 08 f (x) dx â‰ˆ Answer(s) submitted:

â€¢

â€¢

â€¢

â€¢

â€¢ 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:

â€¢ 4.2

â€¢ 6.2

â€¢ 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 â€¢

â€¢

â€¢

â€¢ 1. Use the Trapezoidal Rule to estimate the area.

Answer: T6 =

2. Use Simpsonâ€™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:

â€¢

â€¢

â€¢

â€¢

â€¢ 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. â€¢ 30.5

â€¢ 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) Simpsonâ€™s

Rule, each with n = 4. T4 â‰ˆ

M4 â‰ˆ

S4 â‰ˆ 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?

â€¢ A. trapezoid rule

â€¢ B. left rule

â€¢ C. right rule

â€¢ D. midpoint rule

Is this method an over- or underestimate?

â€¢ A. over â€¢ 11.5

â€¢ 12

â€¢ 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 â€¢ B. under

2. For graph number 2, Which integration method is shown?

â€¢ A. left rule

â€¢ B. trapezoid rule

â€¢ C. midpoint rule

â€¢ D. right rule

Is this method an over- or underestimate?

â€¢ A. under

â€¢ 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?

â€¢ A. over

â€¢ 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?

â€¢ A. under

â€¢ B. over â€¢ U

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ Overestimate

5. Take the sample points from the midpoints.

Answer: M6 = Answer(s) submitted:

â€¢ D

â€¢ A

â€¢ A

â€¢ A

â€¢ B

â€¢ 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. â€¢

â€¢

â€¢

â€¢

â€¢ ? 1. M4

? 2. T4 (score 0.4000000059604645) (d) What can you conclude about the true value of the integral?

â€¢

â€¢

â€¢

â€¢

â€¢ 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:

â€¢ 0.895759

â€¢ 0.908907

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ 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?

â€¢ Choose one

â€¢ Underestimate

â€¢ Overestimate

5. Take the sample points from the midpoints.

Answer: M6 = Answer(s) submitted:

â€¢

â€¢

â€¢

â€¢

â€¢ (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 âˆž

0 Answer(s) submitted:

â€¢ 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 7eâˆ’x dx

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