Question: 3.1.3 Let f: D R and let be a limit point of D. Prove that if limx f(x) = l, then lim f(x)| =

3.1.3 Let f: D R and let be a limit point of

3.1.3 Let f: D R and let be a limit point of D. Prove that if limx f(x) = l, then lim f(x)| = |l|. XX Give an example to show that the converse is not true in general.

Step by Step Solution

★★★★★

3.36 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

R Lim fx l x x EO 380 f... View full answer

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!

Let A be a 4 Ã 3 matrix with a2 = a3. If b = a1 + a2 + a3, then the system Ax = b will have infinitely many solutions. In this case answer true if the statement is always true and false...

If x and y are nonzero vectors in Rn and A = xyT, then the row echelon form of A will have exactly one nonzero row. In this case answer true if the statement is always true and false otherwise. In...

If A and B are n Ã n matrices, then (A - B)2 = A2 - 2AB + B2. In this case answer true if the statement is always true and false otherwise. In the case of a true statement, explain or prove...

Dave, Allen and Matt share profits and losses in the ratio of 50:30:20. Allen withdrew from the partnership December 31. 2014. Capital account balances are as follows: Dave, Capital $ 80,000 Allen,...

Could someone please check my work pup Please state all definitions and theorems that you will need: Definition 5.1.1 Let f: D - R and letc be an accumulation point of D. We say that a real number L...

Could someone please check my work and let me know if I correctly used all of the included theorems that are referenced in the proof Please state all definitions and theorems that you will need:...

Could someone please check my work and let me know if I am correctly using all of the included theorems that are referenced in the proof Please state all definitions and theorems that you will need:...

Could someone please check my work and make sure both cases are correct Please state all definitions and theorems that you will need: Theorem 5.1.13 Let f: D -+ R and g: D -+ R and let c be an...

Could someone please check my work and let me know if I've correctly used all of the included theorems that are referenced in the proof Please state all definitions and theorems that you will need:...

A 250mm diameter well in an unconfined aquifer is pumped at a uniform rate of 3000 V minute. The drawdowns observed at 1m and 100m distances from the centre of the well are 8m and 0.4m, respectively....

You have been hired as a benefit consultant by Jean Honore, the owner of Attic Angels. She wants to establish a retirement plan for herself and her three employees. Jean has provided the following...

13.86 A transformer having 2,400 turns on the primary and 48 turns on the secondary is used as an impedance matching device. What is the reflected value of a 3- load connected to the secondary?

Write a C++ program to calculate the area of the circle given its diameter.

Write a program to produce a sales receipt. Each time the user clicks on a button, an item and its price should be read from a pair of text boxes and displayed in a properly aligned list box. Use a...

Write a program to play a guessing game between another player and your program. Your program will start by initializing an array to 5 fixed values in the ranges of 1-1000 in the array. These values...

For a retailing enterprise that appropriately uses the installment method of accounting for installment sales of merchandise, doubtful installment receivables expense is recognized when: A customer...

Are statements right or wrong? What theorem is applied to find if it's right or wrong. O an n! diverges because an > 0, for all n > 1. n! O lim (+ 1)! "

In the shipping area of the company, the q,a. bill of lading is used to obtain the goods from the warehouse facility and prepare them for shipment to the customer.b. packing slipc. picking ticketd....

Define the sequence (cn) and (sn) inductively by c1(x) := 1, s1(x):= x, and for all n N, x R. Reason as in the proof of Theorem 8.4.1 to conclude that there exist functions c : R R and s : R R such...

Evaluate L(1) by using the sequence (1 + 1/n) and the fact that e = lim(1 + 1/n)n).

Show that lim V Vc for any e >0

If the Prudential Insurance Company surveys its customers to determine the number of children under age 22 living in each household, a. What is the random variable for this survey? b. Is the random...

Use the binomial distribution in which n = 6 and p = 0.3 to calculate the following probabilities: a. x is at most 1. b. x is at least 2. c. x is more than 5. d. x is less than 6.

Dell Computers receives large shipments of micro-processors from Intel Corp. It must try to ensure the proportion of microprocessors that are defective is small. Suppose Dell decides to test five...