1 Let f(x) = 1+x² • (i) Show that ƒ is increasing on [0, ∞). (ii) Use a calculator to compute Jo f(x)dx. 1 2 1}, find a positive integer n such that n ... n' n' 1 1 < [ f(z)dx – Lf(P)< T0
1 Let f(x) = 1+x² • (i) Show that ƒ is increasing on [0, ∞). (ii) Use a calculator to compute Jo f(x)dx. 1 2 1}, find a positive integer n such that n ... n' n' 1 1 < [ f(z)dx – Lf(P)< T0
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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for question 2i) the question actually asks us to show it is decreasing rather than increasing there is a mistake in the image
![2. Let \( f(x) = \frac{1}{1+x^2} \).
(i) Show that \( f \) is increasing on \([0, \infty)\).
(ii) Use a calculator to compute \(\int_0^1 f(x) \, dx\).
(iii) Set \( P = \{0, \frac{1}{n}, \frac{2}{n}, \cdots, \frac{n}{n} = 1\} \), find a positive integer \( n \) such that
\[
0 \leq \int_0^1 f(x) \, dx - L_f(P) \leq \frac{1}{10}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7308ce5-3861-4c47-9233-3364fc93a0c0%2F30f83e09-7954-4944-a617-028b8ed86765%2Fvubqkl8_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let \( f(x) = \frac{1}{1+x^2} \).
(i) Show that \( f \) is increasing on \([0, \infty)\).
(ii) Use a calculator to compute \(\int_0^1 f(x) \, dx\).
(iii) Set \( P = \{0, \frac{1}{n}, \frac{2}{n}, \cdots, \frac{n}{n} = 1\} \), find a positive integer \( n \) such that
\[
0 \leq \int_0^1 f(x) \, dx - L_f(P) \leq \frac{1}{10}.
\]
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