Hank was trying to compute a definite integral using the limit definition, but he got distracted by the beautiful weather and went outside, leaving his work on his desk. You find the following limit written on his paper: n (²-). i=1 (a) What integral was Hank trying to compute? In other words, on which interval [a, b] and for which function f(x) does the above limit equal lim n→∞ 2+ 3i n [ ? f(x) dx b) Can you find a different interval and function that works? (c) If you are told the interval is [-1,5], what must the function f be?
Hank was trying to compute a definite integral using the limit definition, but he got distracted by the beautiful weather and went outside, leaving his work on his desk. You find the following limit written on his paper: n (²-). i=1 (a) What integral was Hank trying to compute? In other words, on which interval [a, b] and for which function f(x) does the above limit equal lim n→∞ 2+ 3i n [ ? f(x) dx b) Can you find a different interval and function that works? (c) If you are told the interval is [-1,5], what must the function f be?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Hank was trying to compute a definite integral using the limit definition, but he got
distracted by the beautiful weather and went outside, leaving his work on his desk. You
find the following limit written on his paper:
lim
n→∞
n
2+
3i
n
Lo fe
α
(a) What integral was Hank trying to compute? In other words, on which interval [a, b]
and for which function f(x) does the above limit equal
3
(²1)
n
f(x) dx ?
(b) Can you find a different interval and function that works?
(c) If you are told the interval is [−1,5], what must the function ƒ be?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2352e4b9-5e06-4a60-ac0f-d436c026c24c%2F496f6236-51b6-449d-8d34-644f7a2cb008%2Fal9ykfk_processed.png&w=3840&q=75)
Transcribed Image Text:Hank was trying to compute a definite integral using the limit definition, but he got
distracted by the beautiful weather and went outside, leaving his work on his desk. You
find the following limit written on his paper:
lim
n→∞
n
2+
3i
n
Lo fe
α
(a) What integral was Hank trying to compute? In other words, on which interval [a, b]
and for which function f(x) does the above limit equal
3
(²1)
n
f(x) dx ?
(b) Can you find a different interval and function that works?
(c) If you are told the interval is [−1,5], what must the function ƒ be?
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