Question: if x is rational 1. Let the function f (x) be defined by: f (x) = lo if x is irrational Show that lim f(x)

if x is rational 1. Let the function f (x) be

if x is rational 1. Let the function f (x) be defined by: f (x) = lo if x is irrational Show that lim f(x) does not exist and therefore that f(x) is not continuous at x = 4. x-74

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!

Answer the following questions about the function 4 E f($)=z,:25 Instructions: - If you are asked for a function, enter a function. - If you are asked to find a: or y-values, enter either a number or...

Results without supporting work will receive no credit. Please show all your work. 1. For the function f x ) graphed here, find the following limits. lim f(x) (a) lim f(x) (b) 2 (x) (c) lim f (x) lim...

2 Let the function f x be defined by f 0 1 and f x for a 0 One can show that the function f is infinitely many times differentiable and that f equals to its Taylor series about x 0 Consider the...

3*+1 -2 for XS1 f (x) = _x? +x+2 for x >1 A piecewise function f (x) is defined by x2 - 3x + 2 Part A: Graph the piecewise function f (x) and determine the range. (S points) Part B: Determine the...

2.For this question, we define the rules f(x)=e 1/x , g(x)= sin(2x) cos(3x) and h(x) = ?(x + 2). (a) Write out the following explicitly. You do not need to give a domain and codomain.i. (f ? h)(x)...

(d) lim [p(x)]f(x) = 1. (1 point) x-+al Suppose that lim f(x) = 0, limg(x) = 0, limh(x) = x-+a 1, lim p(x) = 0o, and lim q(x) = co. (e) lim [p(x) 19(x) = Evaluate each of the following limits. (a)...

1. (01.08 MC) Which of the following is continuous on the interval (-3, co )? (10 points) Of( x ) = * x - 3 - J x - 2 if x 3 Of( x ) = 9-x 3 - VX O f( x ) = Vx+3 2. (01.04 HC) The function f is...

Let (x) = 1 if x is rational and f (x) = 0 if x is irrational. Prove that lim does not exist for any c. There exist rational and irrational numbers arbitrarily close to any c. lim f(x) XC

- Question 1 Which of the following statements is the Extreme Value Theorem? If f attains a local maximum and a local minimum on an interval [a, b), then f is continuous. If f is a continuous...

Single Variable Calculus Review These problems are great for reviewing limits and derivatives from Calculus I in preparation for the upcoming chapter 1. Evaluate the limits if they exist. A. limx...

What is the purpose of preparing common size financial statements?

Let X be a random variable with cumulative distribution function (a) What is the density function fX for X? (b) What is the probability that X if r

Stripped bonds are more sensitive to changes in interest rates than couponbearing bonds. ) True False

The force constant of a massless spring is 2 5 . 0 N / m . A mass of 0 . 4 5 kg is oscillating in simple harmonic motion at the end of the spring

Advanced: CVP analysis and changes in product mix Dingbat Ltd is considering renting additional factory space to make two products, Thingone and Thingtwo. You are the companys management accountant...

Bebida Company has three process departments: Cooking, Blending, and Canning. At the beginning of the year (July 1) there were no work in process or finished goods inventories. The following data are...

A local barbershop cuts the hair of one thousand customers per month. The clients are men and the barbers offer no special styling. During the month of March, one thousand cus tomers were serviced....