I have been quite stuck on this problem could you explain the steps for each part. ### Estimating Area Under a Curve Using Finite ApproximationsTo estimate the area under the graph of the function $ f(x) = 15 - x^2 - 2x $ between $ x = -5 $ and $ x = 3 $, we will use finite approximations in four different scenarios. This involves calculating the area using rectangles, either through a lower sum or an upper sum approach, with varying numbers of rectangles.**a. Lower Sum with Two Rectangles of Equal Width**In this method, two rectangles are used to approximate the area under the curve. The width of each rectangle is determined by dividing the interval $[-5, 3]$ into two equal parts. The height of each rectangle is determined by the minimum value of the function in each interval.**b. Lower Sum with Four Rectangles of Equal Width**Here, we divide the interval $[-5, 3]$ into four equal parts, creating four rectangles. Each rectangle's height is based on the minimum value of the function in its respective interval.**c. Upper Sum with Two Rectangles of Equal Width**For the upper sum, two rectangles are used again with the same width as in part (a). However, the height of each rectangle is decided by the maximum value of the function within each interval.**d. Upper Sum with Four Rectangles of Equal Width**Finally, the interval $[-5, 3]$ is divided into four equal parts as in part (b). The height of each rectangle is based on the maximum value of the function in its interval.By using these methods, we can approach the true area under the curve more closely and learn about the utility of different approximation techniques in calculus.

Given function fx=15-x2-2x, x=-5 and x=3Now part a: Using a lower sum with two rectangles of equal width.Now here n=2 then∆x=3--52=82=4∆x=4So obtained the two intervals= -5,-1,-1,3Now Area =∆xf-5+f3Area =415--52-2-5+15-32-23Area =415-25+10+15-9-6Area =0Now part b: Using a lower sum with four rectangles of equal width.Now here n=4 then∆x=3--54=84=2∆x=2So obtained the four intervals= -5,-3, -3,-1,-1,1, 1,3Now Area =∆xf-5+f-3+f1+f3Area =215--52-2-5+15--32-2-3+15-12-21+15-32-23Area =215-25+10+15-9+6+15-1-2+15-9-6Area =20+12+12+0Area =224Area =48Now part c: Using a upper sum with two rectangles of equal width.Now here n=2 then∆x=3--52=82=4∆x=4So obtained the two intervals= -5,-1, -1,3Now Area =∆xf-1+f-1Area =415--12-2-1+15--12-2-1Area =415-1+2+15-1+2Area =416+16Area =432Area =128Now part d: Using a upper sum with four rectangles of equal width.Now here n=4 then∆x=3--54=84=2∆x=2So obtained the four intervals= -5,-3, -3,-1,-1,1, 1,3Now Area =∆xf-3+f-1+f-1+f1Area =215--32-2-3+15--12-2-1+15--12-2-1+15-12-21Area =215-9+6+15-1+2+15-1+2+15-1-2Area =212+16+16+12Area =256Area =112

Math

Advanced Math

Use finite approximations to estimate the area under the graph of the function f(x) = 15-x - 2x between x = -5 and x 3 for each of the following cases. a. Using a lower sum with two rectangles of equal width b. Using a lower sum with four rectangles of equal width c. Using an upper sum with two rectangles of equal width d. Using an upper sum with four rectangles of equal width

Use finite approximations to estimate the area under the graph of the function f(x) = 15-x - 2x between x = -5 and x 3 for each of the following cases. a. Using a lower sum with two rectangles of equal width b. Using a lower sum with four rectangles of equal width c. Using an upper sum with two rectangles of equal width d. Using an upper sum with four rectangles of equal width

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: how do i solve this question by graphing ? is it consistent or inconsistent ? how many solutions…

Q: It's just one question the solutions Are ther and I need the answer. ThankYou!

A: The population proportions difference CI is, (p^1-p^2)±Zp^1(1-p^1)n1+p^2(1-p^2)n2where p^1 and…

Q: dy dy 2- + 9y = 0 is in the form y(x) = ea* (c cos Bx + c2 sin Bx). Find the values of a and The…

Q: Solve (5x - 3y + 4z = 12 x+y=2z = 8

A: We will use elementary row operations on augmented matrix to find the solution.

Q: An agricultural field trial compares the yield of two varieties of corn. The researchers divide in…

A: The given data is as follows:Sample size, Sample mean of differences Sample standard deviation of…

Q: Using the figure to the right and the following side lengths, find the value of x. RS=3(x-4)+9 and…

A: Given Figure is Here given that RS=3(x-4)+9⇒RS=3x-12+9⇒RS=3x-3andRT=3(3x-9)⇒RT=9x-27

Q: Step C: Use your equation to determine the how many minutes it would take to completely fill the…

A: Given: A table that shows the amount of gallons of water 'w' that was in the tank after 'm' minutes.…

Q: I am going to write the question because it is not clear: Sara and Cara were each given an equation…

A: Equation given to Sara: y=(x+3)2-1 Now ,the correct graph for y=(x+3)2-1 is : Now, we observe that…

Q: 2x -3 35. 2 Use test points to determine the correct shading. х + 2 2x-3 Z2 of 2X-34-2 18-3 7 2UX2)…

A: The given inequality, 2x-3x+2≥2

Q: explain to him how he could do this correctly what should the dimensions of the new poster be.

Q: 4x-4y Evaluate: f.X=5 and y=4 Evaluate: 6x + 3y- 12 when x 6 and y 8

Q: Lis 3 a Solution to レー=8ーメE 3x-8=-7 3.

Q: The following picture represents a network of interconnected pipelines. The arrows represent the…

Q: Can you show me how to solve the problem provided in the picture step by step?

Q: 2b. Solve the following equations for Va and Vb: (Va - 10) (Va + Vb) Va + = 0 5 10 20 (Vb - 5) (Vb +…

A: Explained below

Q: I need help solving q4 parts d-f

A: For 34 people distribution will be : μ = 11σ* = σ/n = 2/34 = 0.3430

Q: Ling has two equations that she found to be valuable models for her research. She thinks that if she…

A: In the given graph, the point of intersection lies in the fourth quadrant. That is x value is…

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

I have been quite stuck on this problem could you explain the steps for each part.

### Estimating Area Under a Curve Using Finite Approximations

To estimate the area under the graph of the function $ f(x) = 15 - x^2 - 2x $ between $ x = -5 $ and $ x = 3 $, we will use finite approximations in four different scenarios. This involves calculating the area using rectangles, either through a lower sum or an upper sum approach, with varying numbers of rectangles.

**a. Lower Sum with Two Rectangles of Equal Width**

In this method, two rectangles are used to approximate the area under the curve. The width of each rectangle is determined by dividing the interval $[-5, 3]$ into two equal parts. The height of each rectangle is determined by the minimum value of the function in each interval.

**b. Lower Sum with Four Rectangles of Equal Width**

Here, we divide the interval $[-5, 3]$ into four equal parts, creating four rectangles. Each rectangle's height is based on the minimum value of the function in its respective interval.

**c. Upper Sum with Two Rectangles of Equal Width**

For the upper sum, two rectangles are used again with the same width as in part (a). However, the height of each rectangle is decided by the maximum value of the function within each interval.

**d. Upper Sum with Four Rectangles of Equal Width**

Finally, the interval $[-5, 3]$ is divided into four equal parts as in part (b). The height of each rectangle is based on the maximum value of the function in its interval.

By using these methods, we can approach the true area under the curve more closely and learn about the utility of different approximation techniques in calculus.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Can i get help with this problem step by step please?
Hello, I have a question about a math problem. I know the formula required, I just don't understand how it applies to this question. What are the steps to solving this?
can you walk me through how to do these 2 problems for my homework
Can you guide me to solve this problem? ''when a number is decreased by 20% the result is 136'' on TI-30XS Caculator, Homework: 6.3 Applications of Linear Equations CC2
Can you show equations and work to please
I don't understand how to solve this problem, can you help me? the problem is 15 -6x for x=2.5