in MyOpenMath. collanyoni to till sowol alt ovi) (d) 3 to 9 using six 1. Estimate the area under the graph of f(x) = x² +7x + 1 from x = rectangles and right endpoints. In your solution, include the exact area of each rectangle. Include a carefully labeled sketch of the graph and the rectangles. (show wod2) bes to aniogbas od osh e $₁=10) 80151 (0) aftol laupo lo ri latanog alv Un brs Vlo 8=* iv ed gnienodo bas sA dahiw laups to slavistnidge a gaian mura memel ods staluola (1) = 3 to x=9 2. Improve your estimate of the area under the graph of f(x) = x² +7x+1 from x = Isbot by using twelve rectangles and right endpoints. In your solution, include the exact area of told each rectangle. Include a carefully labeled sketch of the graph and the rectangles. nottuios odi lo sto sa noitood od to T.& siqmaxa ni I qosa LOY anoitulo eso sal 8. doimo odi waiver lluisto oals binode = 4(x)) 3
in MyOpenMath. collanyoni to till sowol alt ovi) (d) 3 to 9 using six 1. Estimate the area under the graph of f(x) = x² +7x + 1 from x = rectangles and right endpoints. In your solution, include the exact area of each rectangle. Include a carefully labeled sketch of the graph and the rectangles. (show wod2) bes to aniogbas od osh e $₁=10) 80151 (0) aftol laupo lo ri latanog alv Un brs Vlo 8=* iv ed gnienodo bas sA dahiw laups to slavistnidge a gaian mura memel ods staluola (1) = 3 to x=9 2. Improve your estimate of the area under the graph of f(x) = x² +7x+1 from x = Isbot by using twelve rectangles and right endpoints. In your solution, include the exact area of told each rectangle. Include a carefully labeled sketch of the graph and the rectangles. nottuios odi lo sto sa noitood od to T.& siqmaxa ni I qosa LOY anoitulo eso sal 8. doimo odi waiver lluisto oals binode = 4(x)) 3
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![## Calculus Problem Set: Estimating Areas Under Curves
### Problem 1
Estimate the area under the graph of \( f(x) = x^2 + 7x + 1 \) from \( x = 3 \) to \( x = 9 \) using six rectangles and right endpoints. In your solution, include the exact area of each rectangle. Include a carefully labeled sketch of the graph and the rectangles.
**Steps for Solution:**
1. Divide the interval \([3, 9]\) into six subintervals of equal width.
2. Use the right endpoint of each subinterval to determine the height of each rectangle.
3. Calculate the area of each rectangle (height \(*\) width).
4. Sum the areas of all rectangles to estimate the area under the curve.
5. Draw a graph of \( f(x) = x^2 + 7x + 1 \), and overlay the six rectangles, labeling appropriate points and areas.
### Problem 2
Improve your estimate of the area under the graph of \( f(x) = x^2 + 7x + 1 \) from \( x = 3 \) to \( x = 9 \) by using twelve rectangles and right endpoints. In your solution, include the exact area of each rectangle. Include a carefully labeled sketch of the graph and the rectangles.
**Steps for Solution:**
1. Divide the interval \([3, 9]\) into twelve subintervals of equal width.
2. Use the right endpoint of each subinterval to determine the height of each rectangle.
3. Calculate the area of each rectangle (height \(*\) width).
4. Sum the areas of all rectangles to provide a more accurate estimate of the area under the curve.
5. Draw a graph of \( f(x) = x^2 + 7x + 1 \), and overlay the twelve rectangles, labeling appropriate points and areas.
### Additional Notes
- Ensure that your sketches clearly show the function \( f(x) = x^2 + 7x + 1 \), the rectangles used for the approximation, and any relevant points of intersection.
- Label both axes on the graph and denote significant points that are used in the computation of rectangle areas.
The images of the graphs and diagrams should include:
- A continuous curve representing \( f(x) = x^2 + 7x + 1 \).
- Rect](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc195bb-9009-47db-866e-65b6514806e8%2F82d928ba-94a5-442b-aaef-309caba61b16%2F3j1dhe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Calculus Problem Set: Estimating Areas Under Curves
### Problem 1
Estimate the area under the graph of \( f(x) = x^2 + 7x + 1 \) from \( x = 3 \) to \( x = 9 \) using six rectangles and right endpoints. In your solution, include the exact area of each rectangle. Include a carefully labeled sketch of the graph and the rectangles.
**Steps for Solution:**
1. Divide the interval \([3, 9]\) into six subintervals of equal width.
2. Use the right endpoint of each subinterval to determine the height of each rectangle.
3. Calculate the area of each rectangle (height \(*\) width).
4. Sum the areas of all rectangles to estimate the area under the curve.
5. Draw a graph of \( f(x) = x^2 + 7x + 1 \), and overlay the six rectangles, labeling appropriate points and areas.
### Problem 2
Improve your estimate of the area under the graph of \( f(x) = x^2 + 7x + 1 \) from \( x = 3 \) to \( x = 9 \) by using twelve rectangles and right endpoints. In your solution, include the exact area of each rectangle. Include a carefully labeled sketch of the graph and the rectangles.
**Steps for Solution:**
1. Divide the interval \([3, 9]\) into twelve subintervals of equal width.
2. Use the right endpoint of each subinterval to determine the height of each rectangle.
3. Calculate the area of each rectangle (height \(*\) width).
4. Sum the areas of all rectangles to provide a more accurate estimate of the area under the curve.
5. Draw a graph of \( f(x) = x^2 + 7x + 1 \), and overlay the twelve rectangles, labeling appropriate points and areas.
### Additional Notes
- Ensure that your sketches clearly show the function \( f(x) = x^2 + 7x + 1 \), the rectangles used for the approximation, and any relevant points of intersection.
- Label both axes on the graph and denote significant points that are used in the computation of rectangle areas.
The images of the graphs and diagrams should include:
- A continuous curve representing \( f(x) = x^2 + 7x + 1 \).
- Rect
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