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Homework- negar izadiyar Microsoft Edge https://www.mathxl.com/Student/PlayerHomework.aspx homeworkld 48262221 2018 May Term MATH 2413 Section 84489 Homework: Section 2.3 Assignment Score: 0 of 1 pt ?12.3.23 For the given funcion tbx) and valuesind the largestopen intebutn ich th f(x) x2 , L. 64, c=-8, ?#0.35 The largest open interval about c on which the inequality M(x)-LKe holds is® 80f 18 (11 complete) ? HW Score: 22.22%, 6 of 27 pts (Use interval notation. Round to four decimal places.) Enter your answer in the answer box and then click Check Answer Clear All 21 PM part remaining ?

Explanation / Answer

|f(x)- L| < E

|x^2 - 64| < 0.35

|x - 8||x + 8| < 0.35

So, |x+ 8| < 0.35 / |x - 8|

This is of the form |X - c| < delta

So, delta = 0.35 / |x - 8|

delta = 0.35/|-8-8|

delta = 0.35/16 = 0.021875

So,
|x + 8| < 0.021875

So, we have the interval as
-0.021875 < x + 8 < 0.021875

So, -8.021875 < x < -7.978125 ----> ANS

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b)
|X^2- 16| < 0.45

|x + 4| < 0.45 / |X - 4|

Plug in x =-4,
we get delta = 0.45 / |-4 - 4| = 0.0563

And with that
|x + 4| < 0.0563

-0.0563 < x + 4 < 0.0563

-4.0563 < x < -3.9437 ----> ANS

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