Prove that given any n N, there is a function f Cn(R) such that f(n+1)(x)

Question:

Prove that given any n ∈ N, there is a function f ∈ Cn(R) such that f(n+1)(x) does not exist for any x ∈ R.

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:11 AM

See More Questions

Prove that given a real number x there exist unique numbers n and such that x = n - , n is an integer, and 0 < 1.
Suppose that X1, X2, . . . is a sequence of positive integer-valued random variables. Suppose that there is a function f such that for every m = 1, 2, . . . , limn Pr(Xn = m) = f(m), f(m) = 1, and f...
Let E be closed and bounded in R, and suppose that for each x E there is a function fx, nonnegative, nonconstant, increasing, and C on R, such that fx(x) > 0 and fx(y) = 0 for y E. Prove that there...
EX: let X ~ B (5, 0.4) X ~ B (7, 004) Xz ~ B ( 7 0.2) Find the dist. of Now Noint cik Date. 2 No. R X) q X + X 3 X + X
Rita Gonzales won the $41 million lottery. She is to receive $1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5 million after 19 years. The discount rate is 14...
Explain why present value techniques may not be suitable for project evaluation where a business uses Advanced Manufacturing Technologies.
Analyze the chemical process data in Table B. 5 for evidence of multicollinearity. Use the variance inflation factors and the condition number of $\mathbf{X}^{\prime} \mathbf{X}$. Run No. y X x2 X3...
I don't see that in my intermediate accounting text I saved from college, you explain to another member of the accounting division of Dowell Chemical Corporation. This will take some research. Your...
What are some ways a person can save their community?
Consider FASB standards for mergers and acquisitions by not-for-profit organizations. Answer the following questions: a. What is the difference between a merger and an acquisition? b. What is the...
Using the proof of Theorem 7.58, prove that (20) holds if r/2 replaces r. Use part a) to estimate the difference |4 - |, where x0 = 3, f(x) = sin x, and xn is defined by (19). Evaluate x4 directly,...
Prove that if xn-1, xn satisfy (19), then xn is the x-intercept of the tangent line to y = f(x) at the point (xn-1, f(xn-1)).
At the time of her death on September 4, Alicia held the following assets:
Does the emergence of hybrid gangs indicate that the juvenile gang is a form of organized crime?
Is there such a thing as the born criminal? Are some people programmed at birth to commit crimes?
Is conflict inevitable in all cultures? If not, what can be done to reduce the level of conflict in our own society?
Discuss the characteristics of antisocial youths. Do you know anyone who fits the description?
What policy might be the best strategy to reduce teenage drug use: Source control? Reliance on treatment? National education efforts? Community-level enforcement? Harm reduction measures?
A lossy transmission line with characteristic impedance of 75 + j60 is connected to a 200 load. If attenuation is 1.4 Np/m and phase constant is 2.6 rad/m, find the input impedance for = 0.5 m.
How does health insurance risk differ from other types of insurance risk (e.g., automobile or homeowners insurance)? What is the difference between cost sharing and cost shifting? Is retiree health...
A random sample of n = 9 structural elements is tested for compressive strength. We know that the true mean compressive strength = 5500 psi and the standard deviation is = 100 psi. Find the...
A normal population has a known mean 50 and known variance 2 = 2. A random sample of n = 16 is selected from this population, and the sample mean is How unusual is this result?
Let X be a random variable with mean μ and variance σ2. Given two independent random samples of sizes n1 and n2, with sample means X1 and X2, show that is an unbiased estimator for . If X1...
Of what use are government and business budgets to reporters and where would an agency or business hide spending that it wasn't especially interested in sharing with the public? (Please keep in mind...
Mom and Dad owned a house as tenants by the entirety until Dads death last year. Mom then transferred the house to herself as life tenant, with the remainder to her son Sonny as remainderman. Just...
Write a brief story of your life and career to date. Why and how have you become who you are today? What are your strengths and weaknesses? Now write your story again through the eyes of people who...

Prove that given any n N, there is a function f Cn(R) such that f(n+1)(x)

Question:

Step by Step Answer:

The proof is by induction on n It is true for n 0 by Wei...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions