N2 + 2 NA Σε 1 - 2 6 3 i-1 i-1 Problem 1. Calculate 2i+1) using the summation formulas. 30 i=1 Problem 2. Write the expression (but do not fully compute) M5 for f(x) In x on [1, 3]. Problem 3. Show, for f(x) = 3x2 + 4x on [0, 2], that έ (W.3) 8i 1212 2 RN N2 - 1 then compute lim RN. N-oo Problem 4. Here we will find the area under the curve y = e. Remembering that integrals are supposed to be anti-derivatives, we maybe have an idea of what this should be. This will proceed in a number of steps: (a) First, we have to establish a summation formula for N-1 1+ a+ a. . + aN-1 a' i=0 Use the test cases (1- a)(1+a + a2) = 1 - a3 (1-a)(1+ a) 1- a', to conclude gener ally that N-1 1- aN (1 - a) a i-0 N-1 (b) Show that LN ΝΣεν i 0 1- e (c) Using part (a) with a = e/, prove that LN 11 (1-e/N) (d) Using L'Hôpital's Rule, compute lim LN from part (c). N-o0 +
N2 + 2 NA Σε 1 - 2 6 3 i-1 i-1 Problem 1. Calculate 2i+1) using the summation formulas. 30 i=1 Problem 2. Write the expression (but do not fully compute) M5 for f(x) In x on [1, 3]. Problem 3. Show, for f(x) = 3x2 + 4x on [0, 2], that έ (W.3) 8i 1212 2 RN N2 - 1 then compute lim RN. N-oo Problem 4. Here we will find the area under the curve y = e. Remembering that integrals are supposed to be anti-derivatives, we maybe have an idea of what this should be. This will proceed in a number of steps: (a) First, we have to establish a summation formula for N-1 1+ a+ a. . + aN-1 a' i=0 Use the test cases (1- a)(1+a + a2) = 1 - a3 (1-a)(1+ a) 1- a', to conclude gener ally that N-1 1- aN (1 - a) a i-0 N-1 (b) Show that LN ΝΣεν i 0 1- e (c) Using part (a) with a = e/, prove that LN 11 (1-e/N) (d) Using L'Hôpital's Rule, compute lim LN from part (c). N-o0 +
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
Problem 4 please
![N2
+
2
NA
Σε
1
-
2
6
3
i-1
i-1
Problem 1. Calculate 2i+1) using the summation formulas.
30
i=1
Problem 2. Write the expression (but do not fully compute) M5 for f(x) In x on [1, 3].
Problem 3. Show, for f(x) = 3x2 + 4x on [0, 2], that
έ (W.3)
8i
1212
2
RN
N2
- 1
then
compute lim RN.
N-oo
Problem 4. Here we will find the area under the curve y = e. Remembering that integrals
are supposed to be anti-derivatives, we maybe have an idea of what this should be. This will
proceed in a number of
steps:
(a) First, we have to establish a summation formula for
N-1
1+ a+ a. . + aN-1
a'
i=0
Use the test cases
(1- a)(1+a + a2) = 1 - a3
(1-a)(1+ a) 1- a',
to conclude gener ally that
N-1
1- aN
(1 - a) a
i-0
N-1
(b) Show that LN
ΝΣεν
i 0
1- e
(c) Using part (a) with a = e/, prove that LN
11
(1-e/N)
(d) Using L'Hôpital's Rule, compute lim LN from part (c).
N-o0
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7369c9e1-cd27-40fa-b19e-4e793313e403%2F36892dc2-5455-4b97-8c17-7b8dd101fd35%2Fa8pai8.jpeg&w=3840&q=75)
Transcribed Image Text:N2
+
2
NA
Σε
1
-
2
6
3
i-1
i-1
Problem 1. Calculate 2i+1) using the summation formulas.
30
i=1
Problem 2. Write the expression (but do not fully compute) M5 for f(x) In x on [1, 3].
Problem 3. Show, for f(x) = 3x2 + 4x on [0, 2], that
έ (W.3)
8i
1212
2
RN
N2
- 1
then
compute lim RN.
N-oo
Problem 4. Here we will find the area under the curve y = e. Remembering that integrals
are supposed to be anti-derivatives, we maybe have an idea of what this should be. This will
proceed in a number of
steps:
(a) First, we have to establish a summation formula for
N-1
1+ a+ a. . + aN-1
a'
i=0
Use the test cases
(1- a)(1+a + a2) = 1 - a3
(1-a)(1+ a) 1- a',
to conclude gener ally that
N-1
1- aN
(1 - a) a
i-0
N-1
(b) Show that LN
ΝΣεν
i 0
1- e
(c) Using part (a) with a = e/, prove that LN
11
(1-e/N)
(d) Using L'Hôpital's Rule, compute lim LN from part (c).
N-o0
+
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