(a) Given that lim x0 (3x 1)(3x 1)x 2 0 01 0 01 prove that there exists an open interval (a, b) containing 0 such that (3x 1)(3x 1)x 2 0 01 0 for all x 0 in (a, b) (b) Given that lim xc g(x) L, where L 0, prove that there exists an open interval (a, b) containing c such that g(x) 0 for all x c in (a, b)

Question: (a) Given that lim x0 (3x + 1)(3x 1)x 2 + 0.01 = 0.01 prove that there exists an open interval (a, b) containing

(a) Given that

lim _x→0 (3x + 1)(3x − 1)x² + 0.01 = 0.01

prove that there exists an open interval (a, b) containing 0 such that (3x + 1)(3x − 1)x² + 0.01 > 0 for all x ≠ 0 in (a, b).

(b) Given that lim _x→c g(x) = L, where L > 0, prove that there exists an open interval (a, b) containing c such that g(x) > 0 for all x ≠ c in (a, b).

Step by Step Solution

★★★★★

3.53 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Since lim x0 3x 13x 1x2 001 001 we know that there exists a 0 such that if 0 x then 3... 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 Precalculus Questions!

Walmart Hypermarket Co. (WHC or the Entity) owns and operates for offering foods and technology. WHC was formed as a corporation in the 1970s, and all of its outstanding common stock is held by one...

Prove proposition 3.2 assuming that X is finite-dimensional as follows: Let B be the unit ball in X, that is, B = {x: ||x||

Introduction to Financial Accounting Eleventh Edition Charles T Horngren Stanford University Gary L Sundem University of Washington John A Elliott University of Connecticut Donna R Philbrick Portland...

1.3 Homework ! : // 2. -/1 pointsSEssCalcET2 1.3.005. For the function g whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) (b) (c)...

Mohammed Yaaseen Gomdah MATH 203 Winter 2016 F WeBWorK assignment number Practice Problems Midterm W14 is due : 03/04/2016 at 03:00am EST. The (* replace with url for the course home page *) for the...

1. Evaluate the following limits if they exist. 3x2 - 6x + 8 (a lim x-70 2 - 4x + 7 (Do not use L'Hospitals Rule) Answer: 3 (b) lim 2 2 - 8x + 12 2-2 202 - 3x + 2 (Do not use L'Hospitals Rule)...

An open box is made from a square piece of cardboard 12 inches on a side by cutting identical squares from the corners and turning up the sides. Use this information to complete parts a through c. a....

Value Theorem may Pa 9. lim f(x) = 1 10. lim f(x) = f(0) x-+0 alue 1 11. lim f(x) = 2 x-2 x - 2 + 12. lim f(x) = 3 1 /( ) 13. lim f(x) does not exist. 14. lim f(x) = 3 x- 5 In Exercises 15-20, refer...

Can I please have step by step on how to these problems, its my study guide before my test and I dont understand very well all of them Please. 1. a) Use the limit definition of the derivative to find...

I need perfect score, need complete solution each step by step pls i will rate helpful: INTRODUCTION In the previous lesson, we presented and illustrated the limit theorems. We started recalling...

A survey of 25 randomly selected customers found the ages shown (in years). The mean is 32.56 years and the standard deviation is 10.42 years. a) What is the standard error of the mean? b) How would...

The demand and supply functions for hockey sticks are given by QD = 286 20P Q$ = 88 + 40P %3D a. Graph the supply and the demand curves, clearly showing the intercepts and indicating the slopes of...

solve plzz expenditure of \ ( \ $ 1 0 0 , 0 0 0 \ ) . The cost of capital is \ ( 1 2 \ % \ ) . The director of capital budgeting has provided the expected cash flows of the forklifts as follows: \...

E3-6 Affleck Company accumulates the following adjustment data at December 31. 1. Services provided but not recorded total $750. 2. Store supplies of $300 have been used. 3. Utility expenses of $225...

In Exercises use a computer algebra system to find the derivative of the function. f(0) = sin 0 1 - cos 0

In Exercises, find the derivative of the function. (t) = 3 sec(t - 1)

In Exercises, find the derivative of the function. y = 3x - 5 cos(X)

1. We will derive a two-state put option value in this problem. Data: ; (i.e. r=10%). T=1 year. The two possibilities for are 130 and 80. a. Show that the range of is 50 while that of put option is...

A stock with a current price of $12 will either move up to $15 or down to $9 over the next period. The risk-free rate of interest is 3 percent. What is the value of a call option with a strike price...

net price will be $93.10 per share. What is the cost of the preferred stock, including fiotation? Round your answer to two decimal places