Calculus Worksheet

Anonymous
timer Asked: Feb 2nd, 2019
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Question Description

Please see the attached worksheet. It has four calculus problems involving integrals. There are some links provided in the document that may help in solving the problems.

Written Homework : • The formal write-up goes beyond showing your work. Our expectations for your writing are just as high as those held in your humanities courses. Here is an introductory guide to mathematical writing, complete with videos and a tutorial (https://instruct.math.lsa.umich.edu/support/teamhomework/) . The overall idea is that a classmate should be able to read your work and – Identify the problem you are attempting to solve – Follow the step by step process you used to solve the problem – see the practical significance of your answer (for applied problems in particular), and – (most importantly) understand the reasoning behind your approach to the problem These standards may be higher than what you are used to for mathematical writing, but you can achieve them! • Resources you may use on this assignment include your textbook, worksheets/notes from class, group members, the math tutoring center, and your professor. If you use additional resources, like a book or an article, you should document this properly in your write-up. Your intuition about real numbers should be enough to guide you through this part. If you feel uncertain about some of the claims you are making, skim through the first chapter of How We Got from There to Here: A Story of Real Analysis, Theorem 3 in particular. Click here for a link to download the pdf of this text for free (http://textbooks.opensuny.org/how-we-got-from-there-to-here-a-story-of-real-analysis/)

Tutor Answer

Super_Teach12
School: Cornell University

Here is the assignment ;)

1

Calculus worksheet

2

Answer:
a)
𝑅𝑛 = 10 = 1/2 = 0.5
Left Reimann sum = 0. 5( 𝑓(0) + 𝑓(0.5) + 𝑓(1.0) + 𝑓(1.5) + 𝑓(2.0) + 𝑓(2.5))
= 0.5( 3 + 4 + 5 + 6 + 7 + 8)
= 0.5 ∗ 33 = 𝟏𝟔. 𝟓
𝑛 = 100
Right Reimann sum = 0.5( 𝑓(0.5) + 𝑓(1.0) + 𝑓(1.5) + 𝑓(2.0) + 𝑓(2.5) + 𝑓(3.0))
= 0.5( 4 + 5 + 6 + 7 + 8 + 9)
𝐿𝑛 = 0.5 ∗ 39 = 𝟏𝟗. 𝟓
𝑛 = 1024
Exact area under curve = integral (1024 < 3) (from 0->3)
= [𝑥^2 + 3𝑥] (𝑓𝑟𝑜𝑚 0−> 3)
= [ 9 + 9 − 0 − 0]
𝑍𝑛 = 𝟏𝟖
b)
1

(b) Based on your calculations, is ∫0 𝑓(𝑥) dx well defined? Explain your reasoning. If so,
what does it equal?
1

This integral value in which applied of ∫0 𝑓(𝑥) is not well defined since here order of
integration only changed I.e in first part integration is done ln x to x as done on part a. Hence, in
x has the order of limits is changed. This indicates that both are reverse of each other but their
value remains same.
The region of the integration is bounded by 𝑥 = 𝑒 𝑦 = 𝑦 = ln x, x = 0, y = 0 and y =
ln1. Knowing that according to Boman & Rgers, when y=0, x=1(2014).
𝑦 → 0 𝑡𝑜 ln 𝑥
𝑥 → 1 𝑡𝑜 2

3
1

Then I = ∫0 𝑓(𝑥, )𝑑𝑥
𝟏

Hence, ∫𝟎 ...

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Anonymous
Top quality work from this guy! I'll be back!

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