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Chapter 1: Q. 18 (page 153)

Consider the limit expression

limx鈫�0x-3-2x-1

Calculate the limit.

Short Answer

Expert verified

The limit of the expression is鈭�.

Step by step solution

01

Step 1. Given

The given expression is

limx鈫�0x-3-2x-1

02

Step 2. Calculation

The evaluated expression is

limx鈫�0x-3-2x-1=limx鈫�0x-3-limx鈫�02x-1=limx鈫�01x3-2limx鈫�01x=103-210=鈭�-2鈭�=鈭�

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Most popular questions from this chapter

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

limx鈫�-16.

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�-1-f(x)=2,limx鈫�-1+f(x)=2,f(-1)=1.

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�0(5x2-1)=-1

Find a formula for the cost Crof producing a gourmet soup can with radius rand height 5inches, and answer the following questions:

  1. What is the radius of a can that is 5inches tall and costs 30cents to produce?
  2. Your manager wants you to produce 5-inch-tall cans that cost between 20and 40cents. Write this requirement as an absolute value inequality.
  3. What range of radii would satisfy your manager? Write an absolute value inequality whose solution set lies inside this range of radii.

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�3(x2-6x+5)=-4
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