Step 4. Add the areas of all n rectangles Sum of Areas of n rectangles n 2 (5+ **) -→ 2 - 2 + + 4 + n3 i=1 त्रि h² v=1 lim 2n²+ lim (n+1) (2n+1) + 4(n+1) + 3. na len2 2n 2n²² + 3n+1 6n2 lim Zn²+3+1 In 300L lenz lim 2n² n10061² lim 1700 Step 5: take the Limit of the Sum as n approaches infinity Tim + ((ne (2nd) + 1 (plned) + 3+ (n) D(n+1) 4 n₂-n₁=n A nco (13 13-1₁ =12 3 + + 3n 2n = +²0² +²²0 +2 n i1 i=1 + + +2+ len ² + - + (n (no)(2n), 4 (némed) + 2 (W) n² 4n+4 2n 2/1/21 +3] 3] + n →>> W Gen² + 5 + ²/ h] 1 6on² + 5+ 2²/7] 33+0+0+5+0 5½ or 16 square units W lim n=∞L USC 2n² +3m +1 + 4n +4 lenz 2n 4 / +3] 2n 4:22 τη τη
Step 4. Add the areas of all n rectangles Sum of Areas of n rectangles n 2 (5+ **) -→ 2 - 2 + + 4 + n3 i=1 त्रि h² v=1 lim 2n²+ lim (n+1) (2n+1) + 4(n+1) + 3. na len2 2n 2n²² + 3n+1 6n2 lim Zn²+3+1 In 300L lenz lim 2n² n10061² lim 1700 Step 5: take the Limit of the Sum as n approaches infinity Tim + ((ne (2nd) + 1 (plned) + 3+ (n) D(n+1) 4 n₂-n₁=n A nco (13 13-1₁ =12 3 + + 3n 2n = +²0² +²²0 +2 n i1 i=1 + + +2+ len ² + - + (n (no)(2n), 4 (némed) + 2 (W) n² 4n+4 2n 2/1/21 +3] 3] + n →>> W Gen² + 5 + ²/ h] 1 6on² + 5+ 2²/7] 33+0+0+5+0 5½ or 16 square units W lim n=∞L USC 2n² +3m +1 + 4n +4 lenz 2n 4 / +3] 2n 4:22 τη τη
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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Question
I need help in a problem using Riemann Sum. The answer is supposed to be 38/3 square units but I got 16/3 units. Could you point out what I did wrong?
![Step 4. Add the areas of all n rectangles
Sum of Areas of n rectangles
2 (5. - 2) + 2 + 2 + + 2 2
i=1
lim 3
nowo
lim
nex
lim
n700
Step 5: take the Limit of the Sum as n approaches infinity
(2nd) + the (n(ned) + 3 (n)
n₂-n₁=n
13-1₁=12
+3
lim
-
i1
2n
lim 2n² +3n²+1 + 2 + 2/4 +3]
n>00L
lenz
n
11
+
(n+1) (2n+1)
lenz
I'm 2n²+37²1+ #n+4+37-> lim 2n² +34 +1+42 +4 +3]
lim
+²
hral
nvæ
2n
N
4(n+1)
2n
lim Zn²+3^² + √2 + 5 + ²/17]
n00 6n²
len
Con²
i=1
- + (n (n.)(2n+l). 4 (n (ned) + 2 (w)
5½ or
n
33+0+0+5+0
16
3
n
5 + ₂/² + √√/²₂ +5 + ²/17]
+
3
2n
6n²
n
i + 2²2²22
USC
Square units
4:22
2n 2 n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3eb03a80-7cae-4d33-b228-e2e0361c370e%2F693705a9-466f-4f53-afa9-6edaaa3c709f%2Fcfgm9ym_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step 4. Add the areas of all n rectangles
Sum of Areas of n rectangles
2 (5. - 2) + 2 + 2 + + 2 2
i=1
lim 3
nowo
lim
nex
lim
n700
Step 5: take the Limit of the Sum as n approaches infinity
(2nd) + the (n(ned) + 3 (n)
n₂-n₁=n
13-1₁=12
+3
lim
-
i1
2n
lim 2n² +3n²+1 + 2 + 2/4 +3]
n>00L
lenz
n
11
+
(n+1) (2n+1)
lenz
I'm 2n²+37²1+ #n+4+37-> lim 2n² +34 +1+42 +4 +3]
lim
+²
hral
nvæ
2n
N
4(n+1)
2n
lim Zn²+3^² + √2 + 5 + ²/17]
n00 6n²
len
Con²
i=1
- + (n (n.)(2n+l). 4 (n (ned) + 2 (w)
5½ or
n
33+0+0+5+0
16
3
n
5 + ₂/² + √√/²₂ +5 + ²/17]
+
3
2n
6n²
n
i + 2²2²22
USC
Square units
4:22
2n 2 n
![Lenova
Dropbox hw #10
Find the exact area between the graph of f(x) = x² + 2x + 3 and the x-axis on the interval [0, 2] by
taking the LIMIT of a RIEMANN SUM. Show the details of all 5 steps demonstrated on the second video
for class on Thursday April 13.
To receive credit you must use the 5 step process demonstrated in the video and provide the level of
detail provided in the video. Note that the example on the video used the interval [0,1] and in this
assignment we are changing that to [0,2] but that is the only change in the problem. The procedure is
the same.
This counts as 3 dropbox hw assignments and cannot be one of your two dropx. Understanding this 5
step process is very important for calculus 2. Dropbox hw # 10 due Monday April 24.
f(x)=x²+2x+3
ut
f(xi) 37
0
X₁ =a +1AX
Х2= а+ гах
x3 +9+34X
i
Xi- xi 2
Ax=b-a
n
Ax=2-0-2
In general x= a +iAx
xiotich)
X = -
=
Step 1. Partition [a,b) into n
Subintervals
AX AX+
XI
Use f(x)=x²+2x+3
n
a
O
0
xa... Xinh Xi
Xi-1
Step 2. Form a rectangle over each sub-
interval, using LHE, RHE, or midpoints
ith subinterval [x:-1, x)
Xi
equal
2
b
2
Step 3. Write a formula for the area
of the rectange luse area of rectangle)
langth
A=L·W₁₂_
A = f(xi). Ax__width
A = f(²)· (²)
f(x)=x²+2x+3
= [(*)* + 2 ( ² ) +3] ²
12 + 4 +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3eb03a80-7cae-4d33-b228-e2e0361c370e%2F693705a9-466f-4f53-afa9-6edaaa3c709f%2Flh76kgc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Lenova
Dropbox hw #10
Find the exact area between the graph of f(x) = x² + 2x + 3 and the x-axis on the interval [0, 2] by
taking the LIMIT of a RIEMANN SUM. Show the details of all 5 steps demonstrated on the second video
for class on Thursday April 13.
To receive credit you must use the 5 step process demonstrated in the video and provide the level of
detail provided in the video. Note that the example on the video used the interval [0,1] and in this
assignment we are changing that to [0,2] but that is the only change in the problem. The procedure is
the same.
This counts as 3 dropbox hw assignments and cannot be one of your two dropx. Understanding this 5
step process is very important for calculus 2. Dropbox hw # 10 due Monday April 24.
f(x)=x²+2x+3
ut
f(xi) 37
0
X₁ =a +1AX
Х2= а+ гах
x3 +9+34X
i
Xi- xi 2
Ax=b-a
n
Ax=2-0-2
In general x= a +iAx
xiotich)
X = -
=
Step 1. Partition [a,b) into n
Subintervals
AX AX+
XI
Use f(x)=x²+2x+3
n
a
O
0
xa... Xinh Xi
Xi-1
Step 2. Form a rectangle over each sub-
interval, using LHE, RHE, or midpoints
ith subinterval [x:-1, x)
Xi
equal
2
b
2
Step 3. Write a formula for the area
of the rectange luse area of rectangle)
langth
A=L·W₁₂_
A = f(xi). Ax__width
A = f(²)· (²)
f(x)=x²+2x+3
= [(*)* + 2 ( ² ) +3] ²
12 + 4 +
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