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Chapter 1: Q. 15 (page 97)

If x鈭�(1.5,2.5), what is the largest interval I=4-蔚,4+蔚for which we can guarantee that x2鈭�I?

Short Answer

Expert verified

The interval is1.75,6.25.

Step by step solution

01

Step 1. Given information.

The given function isx2.

02

Step 2. Calculation.

For x=1.5

f(x)=x2f(1.5)=(1.5)2 f(1.5)=2.25

So the interval, where 蔚=2.25is:

I=4-蔚,4+蔚I=(4-2.25,4+2.25)I=1.75,6.25

03

Step 3. Conclusion.

Therefore, the interval is1.75,6.25.

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Most popular questions from this chapter

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(3-4x)=3

Write a delta鈥揺psilon proof that proves that fis continuous on its domain. In each case, you will need to assume that 未 is less than or equal to 1.

f(x)=x2

Write each of the inequalities in interval notation:

0<|x-2|<0.1

Calculate each of the limits:

limh鈫�0(1+h)3-13h.

For each functionf graphed in Exercises23鈥�26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

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