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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 +

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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 +
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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