Question: The greatest integer function is defined by [x] = the largest integer that is less than or equal to x. Show that lim x3 [x]

The greatest integer function is defined by [x] = the largest integer that is less than or equal to x.

(For instance, [4] = 4, [4.8] = 4, [] = 3, [2] = 1, [-] = 1.) -

Show that limx→3 [x] does not exist.

(For instance, [4] = 4, [4.8] = 4, [] = 3, [2] = 1, [-] = 1.) -

Step by Step Solution

★★★★★

3.32 Rating (146 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The graph of the greatest integer function is sho... 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

Students Have Also Explored These Related Calculus 6th edition Questions!

Q:

The greatest integer function is defined by [x] = n, where n is the unique integer such that n ¤ x (a) (b) lim [x] lim [x]

Q:

One of the schools sending its team to the tournament has to travel some distance, and so the schools is making sandwiches for team members to eat along the way. There are three choices for the kind...

Q:

Translate the following into symbolic form 1. If Argentina reduces unemployment then if Brazil cuts taxes then both Columbia will support agrarian reform and the Dominican Republic will increase...

Q:

The greatest integer function is defined by f ( x ) = [ x ] , the largest integer that is less than or equal to x . For instance, [ 5 ] = 5 , [ 3 . 2 ] = 3 , [ 5 . 9 9 9 ] = 5 , [ - 0 . 5 ] = - 1 , [...

Q:

(1 point) The symbol [. ] denotes the greatest integer function (also sometimes called the floor function): [x] = greatest integer less than or equal to x. For example, [it] = 3, [3] = 3, and [-1.5]...

Q:

4. Use the given graph of f to state the value of each quantity, if it exists. If it does not exist, explain why. 15-18 . Use a table of values to estimate the (a) lim f(x) (b) lim f(x) (c) lim f(x)...

Q:

please solve: 10. (20 points) Let f(x) = (x]+[-x] where the largest integer function (x] is defined by the largest integer that is less than or equal to r. (a) For what values of a does lim f(x)...

Q:

please solve: 10. (20 points) Let f(x) = (x]+[-x] where the largest integer function (x] is defined by the largest integer that is less than or equal to r. (a) For what values of a does lim f(x)...

Q:

please solve: 10. (20 points) Let f(x) = (x]+[-x] where the largest integer function (x] is defined by the largest integer that is less than or equal to r. (a) For what values of a does lim f(x)...

Q:

Please help me and show work! Use the graph of the greatest integer function, y = LxJ, to nd the limits given below. (3) lim % (1)) lim % e>2* e> 2' (a) Select the correct choice below and ll in any...

Q:

Which of the following statements is true concerning how energydrinks work? Multiple Choice Energy drinks contain vast amounts of carbohydrates and proteinsthat enter into cellular respiration...

Q:

3. THE PACE OF AN ENGINEER IS 0.68m/pace. HE WALKS ALONG THE PERIMETER OF A TRIANGULAR LOT ABC AND FINDS OUT THAT HE MAKES 750 PACES ALONG LINE AB WHOSE BEARING IS $ 280 E AND MAKES 1520 PACES ON...

Q:

Goodness of fit to a standard Normal distribution. Computer software generated 500 random numbers that should look like they are from the standard Normal distribution. They are categorized into five...

Q:

351 For the circuit in Figure P351, find the Thvenin and Norton equivalent circuits 10 www 10 www + 25 V 15 FIGURE P3-51 VT. RT. IN

Q:

Show that 3 is irrational (see problem 77). In problem Show that 2 is irrational. Try a proof by contradiction. Suppose that 2 = p/q, where p and q are natural numbers (necessarily different from 1)....

Q:

Show that the sum of two rational number is rational.

Q:

Shot that the product of a rational number (other than 0) and an irrational number is irrational.

Q:

Hicks Cable Company has a defined benefit pension plan. Three alternative possibilities for pension-related data at January 1, 2016, are shown below: ($ in 000's) Case 1 Case 2 Case 3 Net loss...

Q:

Mirene Athare Soms 2.994 AN 12 Select MO X H MyEducator Tasks Pre-Assessment Part 1 In 2013 County Fron 2018 mples Denton Counter Che North Central Coco Southeast Formatting GE The data on the...

Q:

Tax Drill - Refund of State Income Taxes Janice, a cash basis, unmarried taxpayer, had $1,350 of state income tax withheld during 2022 . Also in 2022 , Janice paid $200 that was due when she filed...