Question: 81. Let f(x) = 0 if x is any rational number and f (x) = 1 if x is any irrational number. Show that f

81. Let f(x) = 0 if x is any rational number

81. Let f(x) = 0 if x is any rational number and f (x) = 1 if x is any irrational number. Show that f is not integrable on [0, 1]. 82. Let f(0) = 0 and f(x) = 1/xif0

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!

Your client is a self-employed attorney who is considering the purchase of a $65,000 automobile that \Viii be used 80% for business. a. What depreciation method and recovery period are used under...

81 Let f x 0 if x is any rational number and f x 1 if x is any irrational number Show that f is not integrable on 0 1

Let f (x) = 0 if x is any rational number and f (x) = 1 if x is any irrational number. Show that f is not integrable on [0, 1].

Let f(x) = 0 if x is irrational and let f (x) = 1/q if x is the rational number p/ q in reduced form (q > 0). (a) Sketch (as best you can) the graph off on (0, 1). (b) Show that f is continuous at...

Question 1 Let X1, X2, .., Xn be a random sample drawn from a distribution with probability density function f (x; 0) = 7 ( 1 + x ) 0+ 1, 0 0 is an unknown parameter. (a) Show that Y, = In(1 + X;)...

D Question 14 2 pts 7. Let f (x) = 5x - 7 and g (x) = 17 b) Find g (f (a)). You must show your work (steps like we did on the class notes) for credit. You may type in yourQuestion 15 1 pts O 7. Let f...

The number of females in medicine continues to show steady increases The number of female physicians in a certain country can be modeled by the functi 1 496 F x 0 798x where x is the number of years...

) Let f ( x ) = { 0 amp; if x is an odd number 1 amp; otherwise Does f ( x ) have a limit as x ? Explain your answer.

MATH 3A03 Assignment #5 Due: Thursday, November 19, in class 1. Let f (x) be the function dened on the interval [0, 2] such that f (x) = 1 for 0 x 1 and f (x) = 2 for 1

12. Let f : X - Y and g : Y - Z. Which of the following statements is not true? (A) If f and g are both 1 - 1 then so is go f. (B) If f and g are both onto then so is go f. C) If go f is 1 - 1, then...

Consider a tie rod transmitting a tensile force F. The corresponding tensile stress is given by = F/A, where A is the area of the cross section. The deflection of the rod is given by Eq. (43), which...

Let A and B be the following matrices. Perform the following operations: 7A= A 6B 3A 2B A= -9 6 4 4-8 7 6 B= -9-8 7 -7-3 9 0 -5

You are the Mine Planning Engineer at a hard rock underground mine using longhole stoping. The production system includes interconnected mining and processing units. Some subsystems are configured in...

Chance Innis did business as Roadrunner Hotshot, renting equipment to oil companies in North Dakota. Inniss sister, Cammie Wold, operated the business. At a restaurant in Williston, Innis and Wold...

If A and B are languages, define A B = {xy| x A and y B and |x| = |y|}. Show that if A and B are regular languages, then A B is a CFL.

Is GDP a good measure of economic welfare? Why or why not?

The following equity investment transactions were completed by Vintage Company during a recent year: Apr. 10. Purchased 11,000 shares of Delew Companys common stock for a price of $60 per share plus...

The driver of the truck has an acceleration of 0.4g as the truck passes over the top A of the hump in the road at constant speed. The radius of curvature of the road at the top of the hump is 98 m,...

Question 7 . Given the following simple maze, convert the maze into a graph. ( 5 points ) Question 8 . Implement depth first search in the maze function in homework 1 . py . ( 2 0 points ) Question 9...

Subjective norms, i.e. the norms of the target group

The temporal rule: The closer temporal proximity we have to an event or action, the more probable it is that the distortion of information is less than if the event or action happened longer ago.

The relevance of the information to the interpreter