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Chapter 1: Q. 33 (page 107)

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

Short Answer

Expert verified

未=蔚5

Step by step solution

01

Step1. Given information. 

We have been given a limit statement as limx鈫�0(5x2-1)=-1.

We have to find 未intermsof蔚.

02

Step 2. Use algebra.

From the given limit statement, we can identify

f(x)=5x2鈭�1c=0L=-1For蔚>05x2鈭�1鈭�(鈭�1)<蔚5x2鈭�1+1<蔚5x2<蔚5x2<蔚x2<蔚5|x|<蔚5For0<|x鈭�0|<未,weget|x|<蔚5Therefore,未=蔚5

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Most popular questions from this chapter

Write each of the inequalities in interval notation:

x2-1+3<0.5

Calculate each of the limits:

limx鈫�01sec-1x.

In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

f(x)=x2,ifx<24,ifx=22x+1,ifx>2.

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�0-f(x)=-1,limx鈫�0+f(x)=1,f(0)=0.

limx鈫�0sinxcosx
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