Let I := [a, b] and let f : I R and g : I

Question:

Let I := [a, b] and let f : I → R and g : I → R be continuous functions on I. Show that the set {x ∈ I : f(x) = g(x)} is closed in R.

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

See More Books

Question Posted: Apr 07, 2016 11:13 AM

See More Questions

Show that the set difference metric given by d(A, B) = size(A B) + size(B A) satisfies the metric axioms given on page 70. A and B are sets and A B is the set difference. 1.4 1.4 1.2 0.8 0.6 0.4 0.2...
Show that the set of optimal strategies for each player is convex.
Show that the set {02n1n | n = 0, 1, 2, . . .} is not regular using the pumping lemma given in Exercise 22.
Runnals National Bank has experienced the following trends over the past five years (all figures in millions of dollars): Input Area: 1 2 3 4 5 Net Income (after tax) 2.65 2.75 3.25 3.65 4.00 Total...
Linda Schiernbeck rented a house from Clark and Rosa Davis. Approximately one month after she moved in, Schiernbeck noticed a discolored area on one of the walls. There was a screw in the middle of...
Use the Trapezoidal Rule and Simpsons Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact...
Explain the effects on income from hedging a foreign currency exposed net asset position or net liability position. LO6
The following accounts appear in the ledger of Celso and Company as of June 30, the end of this fiscal year. Cash ............... $ 15,349 Accounts Receivable .......... 13,810 Merchandise Inventory...
Practice Question 11 The Sun Glass Shack has annual sales of $730,000, and it has $100,000 of accounts receivable.Based on a 365-day year, what is its days sales outstanding? 56 days 54 days 50 days...
A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004...
Let f : R R be defined by f(x) = x2 for x R. (a) Show that the inverse image f-1(I) of an open interval I := (a, b) is either an open interval, the union of two open intervals, or empty, depending...
Show that if f : R R is continuous, then the set {x R : f(x) = k} is closed in R for each k R.
Trace through the binary search algorithm in findInSortedList given the following input. findInSortedList("8",["3","5","7","9","10"])
Find f(x) if y = f(x) satisfies dy dx 60yx and the y-intercept of the curve y = f(x) is 6. f(x)
Data on the gasoline tax per gallon ( in cents ) as of a certain date for the 5 0 U . S . states and the District of Columbia are shown below. State Gasoline Tax per Gallon State Gasoline Tax per...
Write a function report card where the user can enter each of his grades, after which the program prints out a report card with GPA. Remember to ask the user how many classes he took (think - why...
VA= 18/ A c = ? 1. For the arrangement of cable and pulleys in the figure, the velocities and accelerations of two of the bodies involved are indicated. Determine the velocity and acceleration of the...
Suppose there are two electric charges in 2D planeR2; one is on y-axis and the other is on x-axis: 45km 0 p1:=0,p2:=30km.(1) Thechargesareq1=4.5Catp1andq2=3.0Catp2. (a) Determine the electric field...
Which of the following is not a phase in JSF request processing life-cycle? (a) Restore View (b) Apply Request Values (c) Process Validations (d) Prepare Response
2.) Find the Laplace transform of f(t) 7e-St cos 2t +9 sinh2 2t. Use Laplace Table. %3D
When Jennifer's calculator gives a decimal approximation for radical 2 and that assumption is promptly squared, the result is 2. Yet, when that same approximation is entered by hand and then squared,...
The price of a blouse after a 30% reduction if the price before the reduction was P
Fourteen less than some number
You borrowed $15,000 for buying a new car from a bank at an interest rate of 12% compounded monthly. This loan will be repaid in 48 equal monthly installments over four years. Immediately after the...
Discuss how debt restructuring, settlement, or modification works. Discuss the journal entries for debtor and creditor
Could CNL be a viable business? If so, under what conditions and what level of production (and, since production is directly related to production workers, employees)? All information provided for...

Let I := [a, b] and let f : I R and g : I

Question:

Step by Step Answer:

If x n is a sequence in I such that f x n g x ...View the full answer

Introduction to Real Analysis

Students also viewed these Calculus questions