Question: Consider (a) Show that if |x 2| Then explain why this proves that 1 lim x2 X

Consider 1 lim x2 X

(a) Show that if |x − 2|

2 X x-21

(b) Find a 8 >0 such that if 0 < x-2 <6, then <0.01. (c) Let & be the smaller of 1 and 2. Prove the

Then explain why this proves that1 lim X-2 X || 1 2

1 lim x2 X

Step by Step Solution

★★★★★

3.40 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

1 a Since x2 1 it follows that 1 x 3 in particular that x 1 Because x 1 ... 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 4th Questions!

Q:

List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...

Q:

Show that if x > 0 and if n > 2x, then Use this formula to show that 2 2/3 2x+1 (n+ 1)! n!

Q:

Show that if X is a continuous random variable, then where m is the median of X (see Exercise 2.17), EX ml, min E X - al E

Q:

6-9 6. Verify that y1 = 1 +x and y2 = 2 + x + 2 are solutions of the differential equation (1 - 2x - x2) y" + 2(1 +x) y' -2y = 0 then use the method of variation of parameters to solve the equation...

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:

Please answer 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. Please do it on paper bc it's really hard to understand when is written on here. Also, please show step by step how you got that...

Q:

1. (01.02 MC) The number of visitors to a theme park is measured during operating hours. The table shows the number of visitors, v(t), at t hours in one day. For which time of the day is the rate of...

Q:

SECTI In Exercises 19-22, use any method to evaluate the limit or show that it does not exist. 40. lim (x, y ) - (0, 0 lim Boob eolder 20. 10lim Of * 2 - y 2 19. (x, y) - (0,0) Vx2 + 147 grow...

Q:

SECTI In Exercises 19-22, use any method to evaluate the limit or show that it does not exist. 40. lim (x, y ) - (0, 0 lim Boob eolder 20. 10lim Of * 2 - y 2 19. (x, y) - (0,0) Vx2 + 147 grow...

Q:

bilow your work (except for reading information from graphs or graphing). If you use a calculator to get values, state that. Each question is worth 5 points (2 points for the correct answer and 3...

Q:

Antonio Rossi set up a par t-time business on 1 November 2004 buying and selling second-hand sports cars. On 1 November 2004 he commenced business with $66,000 which he immediately used to purchase...

Q:

How much is $102 after a decrease of 100%?

Q:

1 5 Tom is a shareholder of Unit Company. As a shareholder, Tom does not have a right to Select one: a . compensation. b . corporate assets on Unit's dissolution. C . dividends. d . profit from the...

Q:

Describe how entrepreneurship is a solution to global poverty and the liability of poorness.

Q:

If f(x) = 5x, show that 5t- 1

Q:

Suppose the graphs of f(x) = x2 and g(x) = 2* are drawn on a coordinate grid where the unit of measurement is 1 inch. Show that, at a distance 2 ft to the right of the origin, the height of the graph...

Q:

Compare the functions f(x) = x10 and g(x) = ex by graphing both f and in several viewing rectangles. When does the graph of finally surpass the graph of f?

Q:

Let's say there are three hardware stores that sell hammers and there is only one model of hammer on the market. House Depot is a huge big box retailer and can offer this hammer on the market for a...

Q:

Discuss the current economic success status of Peru relative to the COVID-19 crisis.discuss which globalization flow is more relevant for your country and how it may/may not be affected by the...

Q:

What the prot maximizing output level and price if the monopolist had a capacity constraint that limited output to q = 1.5? Show necessary conditions (5 Marks) What is the shadow price of capacity?...