Question: Suppose f is a real function defined on R which satisfies lim h 0 [ f ( x + h ) f ( x h

Suppose f is a real function defined on R which satisfies lim h0[f(x + h) f(x h)]=0(1) for every x in R. Does this imply that f is continuous? Follow these steps

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Let A be a positive constant. Let f(a) be a function such that f() = 3 and f' ( 7) = -5. If g(x) = In((f(x))2 + A sin ac), then g'(7) equals 9 -A 9 6 +A 9 O -30 - A 9 1 OQuestion 3 (1 point) Saved...

Q:

1. Suppose f is a continuous function defined on the interval [0, 10]. If So f (x) dx = 5 + 3v2, and (g f (x) da = 2 + 5V2, use properties of the definite integral to determine the value of fat f (x)...

Q:

Suppose f is a continuous function defined on a rectangle R = [a, b] [c, d]. (a) Write an expression for a double Riemann sum of f. If f(x, y) 0, what does the sum represent? (b) Write the...

Q:

Sections 10.1 and 10.2 Reading Assignment: Sequences and Series Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions...

Q:

ALL SCREENSHOTS ARE NUMBERED EXCEPT FOR THE FIRST ONE! Also, when you respond, please number it as well so I know which of your answers go to. There are 15 TOTAL questions, THANK YOU!! Find the limit...

Q:

ALL SCREENSHOTS ARE NUMBERED EXCEPT FOR THE FIRST ONE! Also, when you respond, please number it as well so I know which of your answers go to. There are 15 TOTAL questions, THANK YOU!! Find the limit...

Q:

2 Statemens-2: ga) 2 function ) Statement-1 & Sttement 2 e coea t 13 I :R R is a function defined by R, where [x] denotes the is correct explanation 2) Statement- & Statement2 te coren twn is not...

Q:

1. Which of the following corresponds to the derivative of f (x) = 7 ng at x = 2, using the primary definition of a derivative, reduced to its simplest form before taking the limit? O A. f' (2) = lim...

Q:

I really need help on these problems. I know it's a lot, but I can't split the question. \fGiven that f [I] and its inverse, f '1 [3} are differentiable functions with f {z} and j" {at} values at x =...

Q:

Question 1 Let y=272 3x. 323 5x2. 72r+3 a) Given that In (y) can be written in the form In (y) = In(A)z + In (B) + In (C) z+ In (D). What are the coefficients A, B, C, and D ? A = B = C= D - b) Using...

Q:

In Chapter 16, Exercise 53 predicted the annual value of the Maine lobster industry catch from the number of licensed lobser fishers. The lobster industry is an important one in Maine, with annual...

Q:

Assume that the average kinetic energy of ions in a plasma is the same as the average kinetic energy of the atoms in an ideal gas. If fusion can begin to occur when the ions approach to within about...

Q:

Saver Help Selling a corporation's stock in public markets for the first time is called 1 points 0 0 : 3 1 3 9 a leveraged buyout eflock Pint Multiple Choice vertical integration. an initial public...

Q:

A particle is moving in three dimensions and its position vector is given by; r(t) = (4, 4t + 2, 3t)i + (4, 5t - 2, 3)2 + (3, 3t + 3, 1t)k where r is in meters and t is in seconds. Determine the...