Suppose that f is a positive function such that f' is continuous. (a) How is the graph

Question:

Suppose that f is a positive function such that f' is continuous.

(a) How is the graph of y = f(x) sin nx related to the graph of y = f(x) What happens as n → ∞?

(b) Make a guess as to the value of the limit

based on graphs of the integrand.

(c) Using integration by parts, confirm the guess that you made in part (b). [Use the fact that, since f' is continuous, there is a constant M such that | f'(x) | ≤ M for 0 ≤ x ≤ 1.]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

See More Books

Question Posted: Jan 13, 2021 06:06 AM

See More Questions

Suppose that f is a continuous real function. a) If 01 f(x) dx = 1, find the exact value of b) If f is C1 on R and 0 f'(x) sin x dx = e, find the exact value of c) If 01 f(x)ex dx = 6, find the exact...
Suppose that f is a function satisfying f(1) = 10, and f'(1.02) = 12. Use this information to approximate 1(1.02).
Suppose that f is a differentiable function. (a) Find d/dx f(f(x)). (b) Find d/dx f(f(x))). (c) Let f|n| denote the function defined as follows: f|1| = f and f[n] = f f[n-1] for n 2. Thus f|2| = f ...
If the Albany highway system described in Problem 29 has revised flow capacities as shown in the following network, what is the maximal flow in vehicles per hour through the system? How many vehicles...
Assume that the largest eigenvalue Î»1 in magnitude and an associated eigenvector v(1) have been obtained for the n Ã n symmetric matrix A. Show that the matrix has the same...
Gainesville Cigar stocks Cuban cigars that have variable lead times because of the difficulty in importing the product: Lead time is normally distributed with an average of 6 weeks and a standard...
The fiscal year of the Eddy Company ends on December 31. Your audit report, dated February 26, is to be delivered to the client on March 9. Listed below are events that occur or are discovered from...
A critically ill patient enters your emergency room, exhibiting signs and symptoms of severe septic shock. In this case, should you immediately begin treatment with a broad-spectrum drug or a...
The LOL Company had the following items in its complex capital structure on December 31, 2023: Preferred stock, $8 par value, $1 dividend, 10,000 shares issued and outstanding. Common stock, $5...
The 2013 financial statements for Royale and Cavalier companies are summarized here: These two companies are in the same business and state but different cities. One-half of Royales sales and...
Evaluate the integral. /2 0 (2 sin) 2 d
Use (a) The Trapezoidal Rule (b) The Midpoint Rule (c) Simpsons Rule to approximate the given integral with the specified value of n. ( e'* dx, n = 8
Estimate the ratio of the translational kinetic energy of the Earth as it orbits the Sun to the rotational kinetic energy it has about its N S axis.
Youre going to build this program in parts. In this exercise, you will build a program that stores a secret word and allows the user to repeatedly guess a letter. Each time the user makes a guess,...
Consider the Boolean function F(W, X, Y, Z) = (0, 1, 2, 4, 6, 10, 12) which has the don't care conditions D(W, X, Y, Z) = (7, 13, 14, 15), the minimum sum-of-products (SOP) expression of Fis: Oa....
Create a Macro using the Macro recorder and Visual Basic statements that will do the following: 1. Create a macro recording the advanced Filter for just those employees located in Chicago Create a...
We all are passionate about something or the other; something that we love doing whenever we get the opportunity. This activity will help you identify that passion or interest of yours. Instructions:...
Introduction and Chapters 1 & 2. View video: Tools of Strategic Analysis Links to an external site. by StudyVids (10:37) Write a 1-2 page reflection paper addressing the following: What are the key...
In the CVS annual report in the Supplement to Chapter 1, refer to the balance sheet and the Summary of Significant Accounting Policies in the notes to the financial statements. 1. Examine the...
What key concerns must functional tactics address in marketing? Finance? POM? Personnel?
Assume that all the given functions have continuous second-order partial derivatives. If z = f (x, y), where x = r cos and y = r sin , show that 1 3z + dr? 1 z r r
Find the directional derivative of f at the given point in the direction indicated by the angle . f (x, y) = xy 3 - x 3 , (1, 2), = /3
Find the directional derivative of f at the given point in the direction indicated by the angle . f (x, y) = y cos (xy), (0, 1), = /4
Write the following system as a vector equation involving a linear combination of vectors. 5x1 2x2 x3 = 2 4x1 + 3x3 = 1
Q6. Determine whether the following improper integrals converge or diverge. [3,3,3] (e) 1 x ln(x) -dx. 1
Find the amount in the account for the given principal, interest rate, time, and compounding period. P=$1,100,r=2.1%,t=7 years; compounded continuously.

Suppose that f is a positive function such that f' is continuous. (a) How is the graph

Question:

lim (fx) sin nx n0 JO

Step by Step Answer:

a Since 1 sin 1 we have f x f x sin x fx and the graph of y f x sin n...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions