Limit Theory image attached 1. Let f(r): , We are interested in verifying that lim f(r) 3.1/3(a) Sketch an accurate graph of f over the domain (0, 2). (You will want a big enoughpicture.)(b) Let e = 1. On the same graph, sketch an error tube about the line y = 3 that wouldbe helpful in evaluating the limit.(c) Solve the equations f(r) = 3-e and f(r) = 3+ c. Which solution is closer toI= 1/3? Demonstrate this on your picture.(d) Given e =1 find a & such that if r- 1/3 <6 then E- 3 0, where e is small. On the same graph., sketch an error tube about theline y = 3 that would be helpful in evaluating the limit.ii. Sketch an accurate graph of f over the domain (0, 2). (You will want a bigenough picture.)iii. Solve the equations f(r) = 3-e and f(r) = 3+e. Mathematically justifywhich solution is closer tor=1/3? Demonstrate this on your picture.iv. Given an e>0 find a & such that if r-1/3| < 8 then -3 < e. Justify youranswer using your work in (iii). (You do not need to state a formal proof. Justjustify that your o works.)

Answered: 1. Let f(r) := We are interested in…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Limit Theory image attached

1. Let f(r): , We are interested in verifying that lim f(r) 3.
1/3
(a) Sketch an accurate graph of f over the domain (0, 2). (You will want a big enough
picture.)
(b) Let e = 1. On the same graph, sketch an error tube about the line y = 3 that would
be helpful in evaluating the limit.
(c) Solve the equations f(r) = 3-e and f(r) = 3+ c. Which solution is closer to
I= 1/3? Demonstrate this on your picture.
(d) Given e =1 find a & such that if r- 1/3 <6 then E- 3 <e = 1. Justify your
answer using your work in (c). (You do not need to state a formal proof. Just
justify that your & works.)
(e) Now do it all again for a general e0.
i. Let e> 0, where e is small. On the same graph., sketch an error tube about the
line y = 3 that would be helpful in evaluating the limit.
ii. Sketch an accurate graph of f over the domain (0, 2). (You will want a big
enough picture.)
iii. Solve the equations f(r) = 3-e and f(r) = 3+e. Mathematically justify
which solution is closer tor=1/3? Demonstrate this on your picture.
iv. Given an e>0 find a & such that if r-1/3| < 8 then -3 < e. Justify your
answer using your work in (iii). (You do not need to state a formal proof. Just
justify that your o works.)

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