Let f(x + y) = f(x) + f(y) for all x and y and suppose that f
Question:
(a) Prove that f is continuous everywhere.
(b) Prove that there is a constant in such that f (t) = mt for all t (see Problem 43 of Section 0.5).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 77% (9 reviews)
a fx fx 0 fx f0 so f0 0 We want to prove that or equivalently But fx fc fx c so L...View the full answer
Answered By
Nazrin Ziad
I am a post graduate in Zoology with specialization in Entomology.I also have a Bachelor degree in Education.I posess more than 10 years of teaching as well as tutoring experience.I have done a project on histopathological analysis on alcohol treated liver of Albino Mice.
I can deal with every field under Biology from basic to advanced level.I can also guide you for your project works related to biological subjects other than tutoring.You can also seek my help for cracking competitive exams with biology as one of the subjects.
3.30+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Calculus questions
-
Let f: X Y be one-to-one and onto. Suppose that f is an open mapping. Then f has a continuous inverse f-1: Y X.
-
Let f: X Y be a linear homeomorphism (remark 2.12). Then there exists constants m and M such that for all x1, x2 X, m||x1 - x2|| || f (x1) - f (x2)|| M||x1 - x2||
-
Let f (x,y) be the probability density function of the continuous random variable (X, Y). If U = XY, show that the probability density function of U is given by dv fu(u)
-
The graph of f is given. (a) Why is f one-to-one? f is one-to-one because it passes the ---Select--- ? (b) What are the domain and range of f ? ?1 ?(Enter your answers in interval notation.) domain ?...
-
List at least three independent software houses (not associated with a computer vendor) that are major players in the software component of the information technology industry. List any software...
-
An incomplete one-way between-groups ANOVA source table is shown below. Compute the missing values. Source SS df MS F Between 56.570 28.285 2.435 Subjects 83.865 10.483 - - Within 16 Total 326.265 26
-
Consider a stock price \(S\) governed by the geometric Brownian motion process (a) Using \(\Delta t=1 / 12\) and \(S(0)=1\), simulate several (i.e., many) years of this process using either method,...
-
During its first year of operations, Ketter Company had credit sales of $3,000,000, of which $400,000 remained uncollected at year-end. The credit manager estimates that $18,000 of these receivables...
-
Image transcription text Use Conservation of Mechanical Energy - JavaLab to collect your data. Introduction: For this lab we want to investigate the conservation of mechanical energy. Our primary...
-
A note payable was executed by Sterling Inc. to Miami Finance Company. Sterling Inc. used 5720,000 of its accounts receivable as collateral for the loan. The contract provided that Miami would...
-
Let D be a bounded, but otherwise arbitrary, region in the first quadrant. Given an angle θ. 0 ¤ θ ¤ Ï/2, D can be circum-scribed by a rectangle whose...
-
Prove that if f (x) is a continuous function on an interval then so is the function |f (x)| = (f (x))2.
-
In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. x = 2t, y...
-
An entity reported net income of EUR 250,000 for 2009. The entity had 125,000 ordinary shares of EUR 1 and 30,000 convertible preference shares of EUR 40 each outstanding during the year. The...
-
Use resolution to answer the query in Example 3.3.4. Data from Example 3.3.4 This example is taken from the predicate calculus and represents a goal-driven graph search where the goal to be proved...
-
Explain the concept of the ACO and its role in the 2010 health reform legislation.
-
What are the pros and cons of hospitalphysician joint ventures?
-
What is the purpose of interaction overview diagrams?
-
Looking at the material in the appendix, what are the primary differences you see between Process 5 (Produce and deliver for manufacturing-oriented organizations) and Process 6 (Produce and deliver...
-
Calculate the electrical conductivity of a fiber-reinforced polyethylene part that is reinforced with 20 vol % of continuous, aligned nickel fibers.
-
Suppose a particle moves back and forth along a straight line with velocity v(t), measured in feet per second, and acceleration a(t). (a) What is the meaning of 60120 v(t) dt? (b) What is the meaning...
-
(a) Write 5 (x + 2x5) dx as a limit of Riemann sums, taking the sample points to be right endpoints. Use a computer algebra system to evaluate the sum and to compute the limit. (b) Use the...
-
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its anti-derivative (take C = 0). cos X xp- 1 + sin x 39. 40.
-
Individual Retirement Account (IRA) Bonds Mutual fund Stocks Futures Defined contribution plans What is it? Level of Risk and Potential Return Minimum investment? Easy to start or stop?
-
1. A company purchased machinery in 2015 for $400,000. Its value in 2018 was $320,000. Assuming the resale value decreases exponentially, what will the value be in 2020? As a part of your solution,...
-
ROA of a company is 8.57%, Total assets end of the year of 2021 are $9.6 million, ROE is 14% and Profit margin of 19.9% what is the firms value of net income? and what is stockholders equity?
Study smarter with the SolutionInn App