Question: 4. (4a) Let A C R and f : A - R. Suppose a is a limit point of A. Prove that if there exist

4. (4a) Let A C R" and f : A - R. Suppose a is a limit point of A. Prove that if there exist parametric curves Y1 : [0, 1] - R" and Y2 : [0, 1] - R" and b1, b2 E (0, 1) such that: . YI(t ) * a ift * b, and Y2(t) * a ift # b2, . lim Y1(t) = lim Y2(t) = a, t-b1 t-b2 . and lim f(r1(t)) # lim f(Y2(t)), t-b1 t- b2 then lim f (x ) does not exist. x-a

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!

The variable resistor R in the circuit of Fig. 11.50 is adjusted until it absorbs the maximum average power. Find R and the maximum average power absorbed. -j100 2 100 2 100 2 100/0 V (+ j100 2 lle

Please help me prove questions 3 and 4. I don't understand it in the slightest, even with examples shown. 3. Prove directly using a suitable modification of Definition 17.4 that 3x - 8 lim - DO....

Suppose that the power series 2 our" and Z bum" converge in (R, R). Let E = {:c G (-R, R) : Zens-r" = anxn}. \"E has a limit point in S, then on = b", for n = 0,1,2, ..., that is, w ix} E aux" = E...

below are my questions..its compl,ete question11 1. Ann is ambiguity-averse and has constant absolute risk aversion a. There is a stock that pays y per unit where y ~ N (u, s') where u e [u, p] is...

Kindly give only correct answers showing your steps 1. (a) Use the Intermediate Value Theorem to show that the equation - sin (x) + sin(x) =-1 has at least two distinct real solutions on (0, ce)....

(1) Prove or disprove : there exist a basis po, pi, p2, pa E PY(R) ( Py(R) is the set of all polynomial over real number with highest possible degree = 3 ) such that none of poly- nomials po. P1, p2,...

do the problem 4.2.1, 4.2.2, 4.2.3 4.2 Pointwise Continuity Let A C R and consider f: A R. In the previous section, we talked about pointwise limits of f at limit points of A. Whenever is in the...

(4) In this exercise we prove the following theorem Theorem. Let E C R and let a E R. If a is a limit point E, then there exists a sequence f : N+ + E\\a} such that fn > a. (a) Briefly explain how...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

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...

A machine that produces hockey pucks costs $20,500 and produces 10 pucks per hour. Two similar companies purchase the machine and begin producing and selling pucks. The first company, Northern Sales,...

A firm is considering building a public good (e.g. a swimming pool). There are n agents in the econ- omy, each with IID private value 0; [0, 1]. Agents' valuations have density f(0) and distribution...

In an income statement, what do Sales and Administrative ( S&A ) expenses typically represent?

Perform a Financial Analysis of the statements from the below financial statement. Write and post a draft of this company report and Financial Ratios and what they tell us about the Company. What is...

Outline a procedure you would follow to identify either an unknown compound OR an unknown acid OR unknown base. Be sure to follow scientific method in your work. Explain whether using solid base...

Write a C++ program that will sort a template array of data using the following guidelines Ask the user for the number of elements, not to exceed SORT_MAX_SIZE = 32 Ask the user for the type of data...

Long time ago, the shells of a particular snail species, which only occurs in Nakanai, New Britain, were used as money on Duke-of-York Island (present-day Atafu, Tokelau Islands, New Zealand). The...

A transshipment problem with 25 origins, 100 destinations and 10 transshipment sites will have (check all that applies) (a) 135 constraints (excluding non-negativity). (b) 1385 constraints (including...

1. To learn how to develop a vision that can be communicated. To gain insight into the importance of game theory for communication strategies.

9. Take a view or attitude that you hold strongly. Search for information that is opposed to this view or attitude. Discuss.

2. In what way can we say that method affects the result we get?