Chapter 5: Fill in the blanks to complete each of the following theorem statements: (page 495)

Q. 17
If $f$ is integrable and monotonic on $[a, b]$ and $n$ is a positive integer, then
role="math" localid="1663147207302" $| E_{L E F T} (n) | \leq | — - — | = |—| ∆ x$

Short Answer

Expert verified

$| E_{L E F T} (n) | \leq | L E F T (n) - R I G H T (n) | = |f (b) — f (a)| ∆ x$

Step by step solution

Given

$f$ is integrable and monotonic on $[a, b]$ and $n$ is a positive integer,

Error Bounds for Left and Right Sums

Let $f$ is integrable and monotonic on $[a, b]$ and $n$ is a positive integer. Then we can bound the error $E_{L E F T} (n)$ of the left sum as follows:

$| E_{L E F T} (n) | \leq | L E F T (n) - R I G H T (n) | = |f (b) — f (a)| ∆ x$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Q. 17
If $f$ is integrable and monotonic on $[a, b]$ and $n$ is a positive integer, then
role="math" localid="1663147207302" $| E_{L E F T} (n) | \leq | — - — | = |—| ∆ x$

Short Answer

Step by step solution

Given

Error Bounds for Left and Right Sums

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Discrete Mathematics

Geometry

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Q. 17If fis integrable and monotonic on a,band nis a positive integer, thenrole="math" localid="1663147207302" |ELEFT(n)|≤|—-—|=—∆x

Short Answer

Step by step solution

Given

Error Bounds for Left and Right Sums

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Discrete Mathematics

Geometry

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Q. 17
If $f$ is integrable and monotonic on $[a, b]$ and $n$ is a positive integer, then
role="math" localid="1663147207302" $| E_{L E F T} (n) | \leq | — - — | = |—| ∆ x$