Writing in Math

Hello 

 

i need this project to be writtin. i posted what is the project about. it’s the first but only not the 4 math porblems . it has 2 options. only one of them is needed. any one of them

 

thank you.

Math 150A Project Spring 2013

Part 1: Writing Assignment.
(20pts) On Titanium you will find two options for your writing assignment. Choose and do only one.

Specifics:
Writing in a math class can sometimes be difficult. Here is a site that you might find
helpful: https://edisk.fandm.edu/annalisa.crannell/writing_in_math/guide.html

Your writing assignment must be typed or written in ink. If you decide to type it, your
assignment should have 1-inch margins and you should type in Times New Roman or
Arial font size 12. Feel free to write in diagrams or notations.

Part 2: Calculations

You must show all your work. No work or lack of work means no credit. This second part must be
written using pencil only. Failure to follow directions will result in loss of points. Work that is too
hard to follow or lack of organization will result in loss of points.

1. (5pts) Grain pouring from a chute at a rate of 8
3

minft forms a conical pile whose altitude is

always twice its radius. How fast is the altitude of the pile increasing at the instant when the pile
is 6ft high?

Differentiate by using logarithmic differentiation

2. (5pts)
 

4
sin 2 3

6

7 5

7

x

x

e

y
x






Choose and do only one of the following

3. (5pts) For the equation

3
1

2

x
y

x




, find dy and y when 1 0.01x and dx 

4. (5pts) Find dy dx by implicit differentiation
2 3

3 3x y xy x  

https://edisk.fandm.edu/annalisa.crannell/writing_in_math/guide.html

The first person to formulate explicitly the ideas of limits and derivatives was Sir Isaac
Newton in the 1660s. But Newton acknowledged that “If I have seen further than other men,
it is because I have stood on the shoulders of giants.” Two of those giants were Pierre Fermat
(1601–1665) and Newton’s teacher at Cambridge, Isaac Barrow (1630–1677). Newton was
familiar with the methods that these men used to find tangent lines, and their methods played
a role in Newton’s eventual formulation of calculus.

The following references contain explanations of these methods. Read one or more of the
references and write a report comparing the methods of either Fermat or Barrow to modern

the curve at the point (1, 3) and show how either Fermat or Barrow would have
solved the same problem. Although you used derivatives and they did not, point out similari-
ties between the methods.

1. Carl Boyer and Uta Merzbach, A History of Mathematics (New York: Wiley, 1989),
pp. 389, 432.

2. C. H. Edwards, The Historical Development of the Calculus (New York: Springer-Verlag,
1979), pp. 124, 132.

3. Howard Eves, An Introduction to the History of Mathematics, 6th ed. (New York:
Saunders, 1990), pp. 391, 395.

4. Morris Kline, Mathematical Thought from Ancient to Modern Times (New York: Oxford
University Press, 1972), pp. 344, 346.

y � x 3 � 2x

EARLY METHODS FOR FINDING TANGENTS ■ 1

This project can be completed
anytime after you have studied
Section 2.1 in the textbook.

WRITING PROJECT: EARLY METHODS FOR FINDING TANGENTS2.1

methods. In particular, use the method of Section 2.1 to find an equation of the tangent line to

WRITING PROJECT
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L’Hospital’s Rule was first published in 1696 in the Marquis de l’Hospital’s calculus
textbook Analyse des Infiniment Petits, but the rule was discovered in 1694 by the Swiss
mathematician John (Johann) Bernoulli

.

The explanation is that these two mathematicians
had entered into a curious business arrangement whereby the Marquis de l’Hospital bought
the rights to Bernoulli’s mathematical discoveries. The details, including a translation of
l’Hospital’s letter to Bernoulli proposing the arrangement, can be found in the book by
Eves [1].

Write a report on the historical and mathematical origins of l’Hospital’s Rule. Start by
providing brief biographical details of both men (the dictionary edited by Gillispie [2] is a
good source) and outline the business deal between them. Then give l’Hospital’s statement of
his rule, which is found in Struik’s sourcebook [4] and more briefly in the book of Katz [3].
Notice that l’Hospital and Bernoulli formulated the rule geometrically and gave the answer in
terms of differentials. Compare their statement with the version of l’Hospital’s Rule given in
Section 3.7 and show that the two statements are essentially the same.

1. Howard Eves, In Mathematical Circles (Volume 2: Quadrants III and IV) (Boston:
Prindle, Weber and Schmidt, 1969), pp. 20–22.

2. C. C. Gillispie, ed., Dictionary of Scientific Biography (New York: Scribner’s, 1974). See
the article on Johann Bernoulli by E. A. Fellmann and J. O. Fleckenstein in Volume II and
the article on the Marquis de l’Hospital by Abraham Robinson in Volume VIII.

3. Victor Katz, A History of Mathematics: An Introduction (New York: HarperCollins,
1993), p. 484.

4. D. J. Struik, ed., A Sourcebook in Mathematics, 1200 –1800 (Princeton, NJ: Princeton
University Press, 1969), pp. 315–316.

WRITING PROJECT THE ORIGINS OF L’HOPITAL’S RULE ■ 1

This project can be completed
anytime after you have studied
Section 3.7 in the textbook.

WRITING PROJECT: THE ORIGINS OF L’HOSPITAL’S RULE3.7

■ www.stewartcalculus.com
The Internet is another source of
information for this project. See
the website and click on History of
Mathematics.

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