Explanation Let the interval [ a , b ] be divided into n subintervals each of width h . Then, average value of f on [ a , b ] for the n subintervals and the given choices of x i is, A = ∑ i = 1 n f ( x i ) n = b − a b − a ( ∑ i = 1 n f ( x i ) n ) = 1 b − a ∑ i = 1 n f ( x i ) ( b − a n ) = 1 b − a ∑ i = 1 n f ( x i ) h Take limit as n → ∞ .

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

See similar textbooks

Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Videos

Question

Chapter 8.CR, Problem 7CR

To determine

To state:

If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.CR, Problem 6CR

Chapter 8.CR, Problem 8CR

Students have asked these similar questions

u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

K Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. x-7 p(x) = X-7 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = OB. f is discontinuous at the single value x= OC. f is discontinuous at the two values x = OD. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - ∞. The limit for the smaller value is The limit for the larger value is The limit for the smaller value is The limit for the larger value does not exist and is not c∞ or -

Chapter 8 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To state: If average value of the function f on [ 1 , 4 ] is given by 1 3 ∫ 1 4 π ( 2 x 2 + 3 ) 2 d x is true or false.

Solution Summary: The author states that if the function f is given by 13displaystyle, it is true or false.

Concept explainers

Videos

To state:

If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.

Want to see the full answer?

Chapter 8 Solutions

To state: If average value of the function f on [ 1 , 4 ] is given by 1 3 ∫ 1 4 π ( 2 x 2 + 3 ) 2 d x is true or false.

Solution Summary: The author states that if the function f is given by 13displaystyle, it is true or false.

Concept explainers

Videos

To state: If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.

Want to see the full answer?

Chapter 8 Solutions

To state:

If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.