Prove that if f: [0, 1] → R is a continuous function, then Find Prove that 1 n n k=1 f lim n1x ())-[² → n 1² we + 2² √e² n³ lim n² n→∞ f(x) dx, as na n + n² wen k k4 + nª || FI∞o

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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(a) Prove that if ƒ : [0, 1] → R is a continuous function, then
n
1
²- ^ ^ ¹ ( ² ) → √ ² ¹ (²
[²
n
k=1
(b) Find
(c) Prove that
lim
N→∞
f(x) dx, as n → ∞o.
x.
1² √e + 2² √e²...+ n² w/en
N³
n
lim n² Σ
n→∞
k=1
k
k 4 + n²
4
ㅠ
Transcribed Image Text:(a) Prove that if ƒ : [0, 1] → R is a continuous function, then n 1 ²- ^ ^ ¹ ( ² ) → √ ² ¹ (² [² n k=1 (b) Find (c) Prove that lim N→∞ f(x) dx, as n → ∞o. x. 1² √e + 2² √e²...+ n² w/en N³ n lim n² Σ n→∞ k=1 k k 4 + n² 4 ㅠ
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