Find the average value of the function f over the given region. f(x.y) = e 7%; R = {(x.y): 0sxs= y): 0sxs,0sys e O A. 7 2 e - 1 O B. 49 OC. 2e -1 O D. e -1
Find the average value of the function f over the given region. f(x.y) = e 7%; R = {(x.y): 0sxs= y): 0sxs,0sys e O A. 7 2 e - 1 O B. 49 OC. 2e -1 O D. e -1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
Find the average value of the function \( f \) over the given region.
**Function:**
\[ f(x,y) = e^{7x} \]
**Region:**
\[ R = \{(x, y): 0 \leq x \leq \frac{1}{7}, 0 \leq y \leq \frac{1}{7} \} \]
**Options:**
- A. \( \frac{e - 1}{7} \)
- B. \( \frac{2(e - 1)}{49} \)
- C. \( 2e - 1 \)
- D. \( e - 1 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04b79f93-1af9-48c9-aa0f-fe250b5d304e%2Fef854fe2-132d-4021-b879-93072b2d92d6%2Fpsq7c4q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the average value of the function \( f \) over the given region.
**Function:**
\[ f(x,y) = e^{7x} \]
**Region:**
\[ R = \{(x, y): 0 \leq x \leq \frac{1}{7}, 0 \leq y \leq \frac{1}{7} \} \]
**Options:**
- A. \( \frac{e - 1}{7} \)
- B. \( \frac{2(e - 1)}{49} \)
- C. \( 2e - 1 \)
- D. \( e - 1 \)
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