Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

i am using the Stewart calculus early transcendentals text and in chapter $2.4 $there is a question:

use the given graph of f to find the number delta such that

if $ 0<|x-5|< \delta$ then $|f(x) -3|< 0.6$

Is the answer: right delta = 0.7 and left delta = 1.0? If so pick the smallest ,correct.....

Any help would be appreciated.

share|improve this question
    
You just use the provided graph: Draw a vertical strip, vertically centered at $y=3$, of height $1.2$. Now draw a horizontal strip centered about $x=5$. What width would this strip have to have in order for the graph of $f$, excluding the point $(5,f(5))$ possibly, to be contained in the rectangle formed by the vertical and horizontal strips? Find the maximum such value using the provided graph. $\delta$ will be half of the width found. –  David Mitra Feb 3 '13 at 17:25
    
If they give you $f(x)$ by a graph, presumably you should estimate the points where the condition just starts to fail by eye... –  vonbrand Feb 3 '13 at 17:25
add comment

2 Answers 2

up vote 1 down vote accepted

How far can you get away from $x=5$ before the function's value exceeds 3.6 or is below 2.4?

share|improve this answer
    
so right delta = 0.7 and left delta = 1.0? –  codenamejupiterx Feb 3 '13 at 21:50
    
I can't say without seeing the graph, but, you are correct (as you stated in your edit to the question) that you should pick the least of the two. –  Jonathan Feb 4 '13 at 0:36
    
Thank You for your help! –  codenamejupiterx Feb 4 '13 at 6:58
add comment

Maybe this will help ?

You want something in the nature of :

5 - delta < x < 5 + delta

and 3-0.6 = 2.4 < f(x) < 3 + 0.6 = 3.6

If they gave you the graph for f(x), I think that implies you can estimate the bounds (thus lead to the finding of delta) by some eye-balling (Since you already know the lower & upper bound for f(x), using the 2nd condition that I listed above). Using the strategy as in David's comment also works.

share|improve this answer
    
so right delta = 0.7 and left delta = 1.0? –  codenamejupiterx Feb 3 '13 at 21:58
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.