Question: If the function f is defined by Prove that limx0 f(x) does not exist. 0 if xis rational l if xis irrational

If the function f is defined by
If the function f is defined byProve that limx†’0 f(x)

Prove that limx†’0 f(x) does not exist.

0 if xis rational l if xis irrational

Step by Step Solution

★★★★★

3.39 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Suppose that fx L Given 12 there exists 0 such that 0 x f... View full answer

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

Document Format (1 attachment)

Word file Icon

786-C-L-D (335).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

If the function f is defined by Prove that limx→0 f (x) does not exist. Jo if x is rational ! if x is irrational f(x) =

Q:

A function f is defined by Find the minimum value of f. /(x) = (" cos t cos(x-t) dt 0 2

Q:

A function f is defined by f(x) = 1 + 2x + x2 + 2x3 + x4 + ... that is, its coefficients are c2n = 1 and c2n+1 = 2 for all n ( 0. Find the interval of convergence of the series and find an explicit...

Q:

In Exercises 3540, nd the limit (if it exists). If the limit does not exist, explain why. r3+l, t-(l 36. 11m [[x - 1]] 39. }1_]'T]1h[l'),WheTeh(f) = {%[1+ 1), t 2 1 zM [n Exercises 4152, determine...

Q:

Let b > 0 and let (x) = F(xG(b)) with F as in Exercise 117. Use Exercise 116 (f) to prove that (r) = b r for every rational number r. This gives us a way of defining b x for irrational x, namely b x...

Q:

8. True/False questions For each of the following, answer whether the statement is True of False and then give a brief justification of your answer. Such questions may appear on your exam, with or...

Q:

Prove that the function f defined by Is not integrable on [0, 1] f(x) = { 1 if x is rational 0 if x is irrational

Q:

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Q:

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

Q:

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Q:

John and Jay agree to be partners where their profits are shared in a ratio of 3:5, respectively. If Jay receives F^(45),500, how much profit should John receive?

Q:

Usually, which outweighs the other in decentralization advantages or disadvantages?

Q:

Prairie Dog Corporation ( PDC ) , an oil drilling company, has a key - person variable universal life policy on Digger Phelps, its vice - president of drilling operations. The owner and beneficiary...

Q:

A random variable X has the probability density function f (x) = 2 9 x(3 x), for 0 x 3. Find the probability density function for Y = X2 1.

Q:

Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral. a. Entry 80 b. Entry 39 cos 5x cos 2x dx;

Q:

The region under the curve y = sin2x from 0 to is rotated about the x-axis. Find the volume of the resulting solid.

Q:

Verify Formula 53 in the Table of Integrals (a) by differentiation and (b) by using the substitution t = a + bu.

Q:

Bethesda Mining Company reports the following balance sheet information for 2013 and 2014. Required: Prepare the 2013 and 2014 common-size balance sheets for Bethesda Mining. (Do not round...

Q:

Please complete the following tables using canadian tax laws It is January 3, 2022. Hayley Stewart, the controller for the Fraser Operating Group, is reviewing the GST compliance requirements for the...

Q:

Mining Corp has 9 million shares of common stock outstanding, 350000 shares of preferred stock outstanding with $9 annual stated dividend, and 120000 bonds outstanding with a 10% semiannual coupon...