Q. 15 Fill in the blanks: Let f be a ... [FREE SOLUTION]

Chapter 7: Q. 15 (page 652)

Fill in the blanks: Let f be a function with domain $[1, 鈭�)$ . If the function $|f|$ is and , and if converges, then the series _ converges absolutely.

Short Answer

Expert verified

On completing the fill in the blanks, we get, "Let f be a function with domain $[1, 鈭�)$ . If the function $|f|$ is monotonically and decreasing , and if $\lim_{x 鈫� 鈭�} f (x) = 0$ converges, then the series ${鈭�}_{x = 1}^{鈭�} f (x)$ converges absolutely. "

Step by step solution

Step 1. Given information.

Consider the given question,

Domain is $[1, 鈭�)$ .

Step 2. Fill in the blanks.

If the function $|f|$ is monotonically decreasing and $\lim_{x 鈫� 鈭�} f (x) = 0$ and the integral ${鈭�}_{x = 1}^{鈭�} f (x) d x$ converges, then the series ${鈭�}_{x = 1}^{鈭�} f (x)$ converges absolutely by integral test.

Therefore, the first blank is completed by monotonically and decreasing, second blanks by $\lim_{x 鈫� 鈭�} f (x) = 0$ and third is ${鈭�}_{x = 1}^{鈭�} f (x)$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Fill in the blanks: Let f be a function with domain $[1, 鈭�)$ . If the function $|f|$ is and , and if converges, then the series _ converges absolutely.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Fill in the blanks.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

91影视

Fill in the blanks: Let f be a function with domain [1,鈭�). If the function f is ______ and ______ , and if ______ converges, then the series _______ converges absolutely.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Fill in the blanks.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Fill in the blanks: Let f be a function with domain $[1, 鈭�)$ . If the function $|f|$ is and , and if converges, then the series _ converges absolutely.