Premium Essay

In: Science

Submitted By verdant

Words 472

Pages 2

Words 472

Pages 2

On the interval [2, 9] integrate:

∫ (3x²-4) dx = x³-4x = (729-36) - (8-8)

= 693+0 = 693

Average value over the interval is

693

Question two

Find the area of the shaded region. 2) f(x) = -x3 + x2 + 16x, g(x) = 4x

-x3 + x2 + 16x = 4x

-x3 + x2 + 16x-4x = 0

-x3 + x2 + 12x = 0 x(-x2+ x + 12) = 0 x=0 or x2-4x+3x-12 X(x-4)+3(x-4) = 0 x=0, x=-3,x=4

A = ∫ ((x2- x -12) dx = [x3/3- x2/2 -12x] + [x3/3- x2/2 - 12x]

A = [-9 + 4.5 + 36] + [64/3 – 8 – 48]

A = [31.5] + [-34.666]

A= 3.16666units sq

Question three

Find f(4, 3, 6) when f(x, y, z) = 4x2 + 4y2 - z2.

We substitute x, y and z with 4, 3 and 6

F(x,y,z)=4x2+ 4y2+ z2 =4(4)2+ 4(3)2+ (6)2 =4(16) + 4(9) +36 = 64 + 36 +36 = 136

Question four

Suppose the supply and demand functions of a certain item are given by S (q) = 4q + 2 D (q) = 14 - q2. Find the requested information. (3 pts.) a) Equilibrium Point Equilibrium point is where quantity demanded = supply supplied 14 - q2 = 4q + 2 - q2 -4q +12=0 q2 + 4q -12=0 q2 +6q-2q -12=0 q(q+6) -2(q+6) =0

(q-2)(q+6)= 0

Q=2 or q = -6

The equilibrium point is where q = 2.

Get me your contacts so that next time we can talk. Please send it inform of a document. Thanks b) Producer Surplus 14 - q2 > 4q + 2 - q2 -4q +12>0 q2 + 4q -12>0 q2 +6q-2q -12>0 q(q+6) -2(q+6) >0 (q-2)(q+6)> 0 q=2 or q = -6

Produder surplus is at point above 2 c) Consumer Surplus 14 - q2 > 4q + 2 - q2 -4q +12>0 q2 + 4q -12>0 q2 +6q-2q -12>0 q(q+6) -2(q+6) >0 (q-2)(q+6)> 0 q>2 or q >-6

Produder surplus is at point above 2

14 - q2 < 4q + 2 - q2 -4q +12<0 q2 + 4q -12<0 q2 +6q-2q -12>0 q(q+6) -2(q+6) < 0 (q-2)(q+6)< 0 q<2…...

Free Essay

...SOME DIFFERENTIAL CALCULUS YOU MAY NEED 1. THE FIRST DERIVATIVE 1.1 For a power function y = f(x) = Axm , dy/dx = Amxm-‐1 This holds for ALL values of m. If m= 0, i.e.-‐ y = Ax0 (which is equal to A) dy/dx = A0x0-‐1 = 0. So the derivative of a fixed (constant) quantity is zero Examples: a. For a linear function of a single variable: y = f(x) = ax dy/dx = a Thus for a cost function C(q) = 4q, the marginal cost dC/dq = 4 b. For an affine (linear with intercept) function: y = f(x) = c + mx dy/dx = m (note that the c vanishes) For a cost function with a fixed cost, C(q) = 180 + 3q, dC/dq = 3 c. We can also get a function of mixed higher order polynomials y = f(x) = a + bx + cx2+ dx3 dy/dx = b + 2cx + 3dx2 For a cost function C(q) = 150 + 34q3 + 20q2, ......

Words: 845 - Pages: 4

Free Essay

...Justin Ladd Calc 1 4/12/2011 Mini Project 2 Mini Project 2 For this project I took a different approach. I wanted to try something that was a little more changeling for me and at the same time I wanted a problem that would make me think. I know for some people that this may not seem to be that hard of a problem but for me these types of problem are difficult. I wanted to pick a problem that pertained to my major, which is Mechanical Engineering but that did not work out to well for me on the last project because I ended up treating the problem like an engineering problem and not a calculus problem, so with that being said that’s one reason that I picked this problem. The other reason that I choose this problem is that it seemed interesting to me and it is a story problem. For me personally I struggle with story problems and have difficulty comprehending what the problem is asking me to find. So let me tell what the problem is and then I will explain how I think it is related to the curriculum and a real world phenomenon: A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min, how fast is the water level rising when the water is 30 cm deep? This problem is related to the curriculum because it is about linear approximation and differentials (Stewart). We covered this section is......

Words: 983 - Pages: 4

Free Essay

...Section 1.2 (Page 87) (Calculus Book): 14, 23, 26, 29, 30, 31, and 32 14.��������→�� ���� +���� −����+�� ���� −����+�� ���� + ���� − ���� + �� = ������ �� ��→�� �� − ���� + ���� − �� − ���� + �� ���� − ���� + ������ − ���� − ���� + �� = ������ �� ��→�� �� �� − �� + �� �� − �� − �� �� − �� ���� �� − �� + ���� �� − �� − �� �� − �� = ������ ��→�� ���� + �� − �� �� − �� ���� �� − �� + ���� �� − �� − �� �� − �� = ������ ��→�� �� − �� �� − �� �� − �� ���� + ���� − �� = ������ ��→�� �� − �� �� − �� ���� + ���� − �� − �� = ������ �� ��→�� �� + ���� − �� − �� = ������ ��→�� �� �� + �� − �� �� + �� �� �� + �� − �� �� + �� �� + �� �� − �� �� + �� �� − �� �� + �� �� + �� �� = = �� + �� �� + �� �� ��+�� ���� −���� = ������ ��→�� = ������ ��→�� 23 ������ ��→�� = ������ ��+�� ��→�� ��+�� ��−�� ⟹ ������ ��→�� �� �� �� = = = ������������������ ∴ ���������� ����������′ �� ���������� �� − �� �� − �� �� ��−�� ���� −����−�� 26 ������ ��→�� = ������ ��→�� ��−�� ���� −����+����−�� = ������ ��−�� ��→�� �� ��−�� +�� ��−�� Page | 1 = ������ ��→�� �� − �� �� − �� −�� �� = = = �� − �� �� + �� �� − �� �� + �� �� × �� �� ∴ ���������� �������� ������ ����������. �� − �� ��−�� �� �� = ������������������; 29������ ��→�� ��−�� ��−�� = ������ ��→�� = ������ ��→�� ��−�� ��+�� ��−�� = ������ ��→�� �� + �� = �� + �� = �� + �� = �� ��−�� 30������ ��→�� ��− �� = ������ �� ��......

Words: 590 - Pages: 3

Free Essay

...Project Gutenberg EBook of Calculus Made Easy, by Silvanus Thompson This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: Calculus Made Easy Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differentia Author: Silvanus Thompson Release Date: October 9, 2012 [EBook #33283] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK CALCULUS MADE EASY *** Produced by Andrew D. Hwang, Brenda Lewis and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) transcriber’s note Minor presentational changes, and minor typographical and numerical corrections, have been made without comment. All A textual changes are detailed in the L TEX source ﬁle. This PDF ﬁle is optimized for screen viewing, but may easily be A recompiled for printing. Please see the preamble of the L TEX source ﬁle for instructions. CALCULUS MADE EASY MACMILLAN AND CO., Limited LONDON : BOMBAY : CALCUTTA MELBOURNE THE MACMILLAN COMPANY NEW YORK : BOSTON : CHICAGO DALLAS : SAN FRANCISCO THE MACMILLAN CO. OF CANADA, Ltd. TORONTO CALCULUS MADE EASY: BEING A......

Words: 55659 - Pages: 223

Free Essay

...Aus UNI VAM2132 - Manufacturing materials: Laboratory 1 Name: Santoss Student ID: XXXXX High Pressure die Casting: Aluminium High Pressure Die Casting Aluminium: High Pressure Die Casting (HPDC) is an industrial metal casting process categorized by forcing molten metals under high pressure in a mould cavity. Mould cavity is made of two hardened tool steel dies which have been properly machined into desired shape and work similarly to an injection during the process. HPDC is most widely used casting process for aluminium casting alloys. There are two types of HPDC: Hot-chamber and Cold-chamber die casting. Variations on these two types include: 1. Hot-chamber die casting: is the more popular of the two die casting processes. In this process, the cylinder chamber of the injection device is completely dipped in the molten metal immersion. A gooseneck metal feed system draws the molten metal into the die cavity. Fig. 02 Hot Chamber High pressure die casting. http://www.engineerstudent.co.uk Direct immersion in the molten bath allows for quick and appropriate mould injection, it also results in increased corrosion proneness. Due to this point, the hot-chamber die casting process is best appropriate for applications that utilize metals with low melting points and high fluidity. Good metals for the hot-chamber die casting process include lead, magnesium, zinc and copper. 2. The cold-chamber die casting process is very similar to hot-chamber die......

Words: 1415 - Pages: 6

Premium Essay

...having favorable Learning Environment to the student particularly in the University of Mindanao. This research is merely concerned to the Engineering student of University of Mindanao of how they react with a certain environment in this University. As a team researcher, we also aimed to bring important information not only to the student but also to the faculties and staff of University of Mindanao on how they address the impact of having conducive environment to the particular student. In the process of continuous learning, learning environment plays important rule in nurturing student to become a better citizen in this world. Since, we are prone in the digital period with high-tech facilities and equipment. We are obliged to take the challenge of learning as our first priority to develop as an individual. The first learning experiences in school create a foundation for successful reading by fostering favorable impression of what is to be derived from the book and language use. Programs should also accommodate children’s varied stages of social and intellectual development. Research has shown that children with rich experiential and language backgrounds are better prepared for beginning reading than children who lack such background (Grolier Encyclopedia, 1995). Choosing capable workstations acoustically sound cork bulletin boards, and other classroom furniture, as well as considering different ways to think of and use space and student desk layout and being alert to......

Words: 2166 - Pages: 9

Free Essay

...Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of......

Words: 561 - Pages: 3

Free Essay

...year 1965, offers a wide variety of degrees, both in the undergraduate and graduate level. Ever since, PLM produces competitive students that can cope up and excel with the changing needs of our society. Some of the courses that PLM offers are engineering courses such as chemical, civil, computer, electrical, electronics, mechanical and manufacturing engineering. Every year, about 500 freshmen enroll in these engineering courses. However, due to the complexity of the curriculum and other factors, a significant decrease in the number of engineering students are perceived every school year. This results to a low graduation rate. This phenomena reflects the existing condition that the whole country is facing, a high enrollment rate but low graduation rate. With that being stated, this study aims to determine the factors that affect the attrition rate of engineering students per degree program. Supplementary factors to be determined includes both the intrinsic and extrinsic factors. Intrinsic factors include the overall wellness of the student, health, skills and personality, time management and such. Moreover, extrinsic factors includes students’ behavior in interaction with the society like having a social life, financial problem, long travel time, and the like. The aim of this study is to determine the major factors which greatly influenced the students and in the long run might cause further increase in attrition rate. STATEMENT OF THE PROBLEM General......

Words: 574 - Pages: 3

Free Essay

...for my masters here at NMSU. In order to meet the prerequisites for the MBA program, I needed to take calculus and I’m glad I did because I wouldn’t have otherwise. Everything I learned in calculus challenged me to think critically and in another sense that I hadn’t known before. Being able to apply calculus to optimize a business’s performance, whether it be through current performance or future expectations is huge for any business. (Saiz, 2001) Since I can remember I’ve always felt like I am supposed to help my dad’s business despite it not really being my passion. I have found it to be difficult to work in that kind of environment. My dad’s business has done really well but it’s not something I love doing and honestly I don’t want anything given to me because of my dad’s successes, I want to do it on my own. The knowledge I have learned through college and the amount I have grown to be independent has made me realize that I can do anything. I have since decided to start my own in business in something I am extremely passionate about. Using calculus to determine rates to charge potential customer for optimal profits can really help my business get started. I think many people that start businesses jump into it without having structure and often times fail. I have found many tools and resources such as calculus to be very beneficial to the success of a business. Calculus will help my business predict maximum sales for a given service and help determine minimum costs......

Words: 989 - Pages: 4

Free Essay

...Many gifted students such as myself accredit Gottfried Leibniz to be the precursor of their impending demise. Mr. Leibniz is the curator of Calculus, the idol of integrals, the devil of derivatives. Calculus is the study of change, and since it’s inception in the 17th century, it has changed the world. I also believe it to be the keystone to changing our future. Studies and general common sense show that our world is quickly deteriorating, and although judgements vary, it is no secret we will soon be evicted from Earth. Our future relies in physics, as it is our only foundation for understanding the world outside our world, and Calculus is our foundation for understanding our sole gateway. Physics would be just a game if it weren’t for Calculus, and we need the higher level of physics to comprehend what is outside our atmosphere and galaxy. Once the day approaches where humanity’s existence is futile and we are being shipped off to our new home in some foreign galaxy, Calculus will be our intellectual voucher to save humanity and all of it’s progression since our conception. Yes, I like all, have suffered through its limits and fundamental theorems, but I, unlike all, see the value in the deed. People love to hate it, but what I’ve learned while racing at the highest level, is that you need to embrace the struggle, and use that struggle to achieve something greater than yourself. I’ve lost entire days of my life studying for seemingly pointless tests, struggling to grasp......

Words: 501 - Pages: 3

Free Essay

...BATANGAS FACTORS AFFECTING THE ACADEMIC PERFORMANCE OF ENGINEERING STUDENTS In partial Fulfillment for the Requirements for Methods of Reasearch by Carandang, Castillo, Gonda, Santos, I. Introduction Engineers nowadays are in demand to lots of companies here and abroad. In fact, thousands of engineering graduates and board passers work mostly in other countries. This is the reason why lots of students took engineering courses. Engineering has always been considered as a very difficult course by most of the students. It’s almost always the last thing that will come to the minds of the students when it comes to choosing their course or program. Engineering, as a program has a lot of difficulties within its name. There are lots of math and science subjects and instructional activities that students will really find it difficult to pass. It requires a great responsibility in achieving the title “Engineer”. Some students who are already taking up engineering doesn’t know the hardships that they are still about to face, that’s why a large number of students tend to have a low academic performances. The field of engineering has become so diverse in recent years that a definition is not easy to come by. Engineers still build skyscrapers, design machinery, and oversee public works. They also address society's needs and problems on a number of other scales with a unique blend of technology and science. At the macro level, environmental engineers are......

Words: 3617 - Pages: 15

Premium Essay

...In a world where we depend on machines more than ever before, mechanical engineers keep things running. Mechanical Engineering is one of the broadest professions. The women and men in the mechanical engineering profession work in almost every industry, in private practice, in government, in medicine, in law, and in universities. Mechanical engineers touch almost every aspect of technology. They create machines, products and technological systems that benefit society. Their work can take them around the world - anywhere there are machines, there are mechanical engineers. The above statements prove that mechanical engineering is not an easy profession. This is the reason why we should consider the spiritual and educational needs. Spirituality means different things to different people. Some persons have religious needs. Spirituality can refer to an ultimate or an alleged immaterial reality an inner path enabling a person to discover the essence of his/her being; or the “deepest values and meanings by which people live.” Educational needs, on the other hand are those that has something to do with their attitudes and technique in studying the subjects of the said profession. This education comes from the professors, parents and all the people that surround us. Special education is the education of students with special needs in a way that addresses the students' individual differences and needs. Ideally, this process involves the individually planned and systematically......

Words: 1851 - Pages: 8

Premium Essay

...Predicting student academic performance has long been an important research topic in many academic disciplines. The present study is the first study that develops and compares four types of mathematical models to predict student academic performance in engineering dynamics – a high-enrollment, high-impact, and core course that many engineering undergraduates are required to take. The four types of mathematical models include the multiple linear regression model, the multilayer perception network model, the radial basis function network model, and the support vector machine model. The inputs (i.e., predictor variables) of the models include student's cumulative GPA, grades earned in four pre-requisite courses (statics, calculus I, calculus II, and physics), and scores on three dynamics mid-term exams (i.e., the exams given to students during the semester and before the final exam). The output of the models is students' scores on the dynamics final comprehensive exam. A total of 2907 data points were collected from 323 undergraduates in four semesters. Based on the four types of mathematical models and six different combinations of predictor variables, a total of 24 predictive mathematical models were developed from the present study. The analysis reveals that the type of mathematical model has only a slight effect on the average prediction accuracy (APA, which indicates on average how well a model predicts the final exam scores of all students in the dynamics course) and on......

Words: 432 - Pages: 2

Free Essay

...organization like NCC, NSS, NYKS, other (please specify and enclose relevant documents thereof) ANY DISTINGUISHED WORK DONE, if so, please state, clearly. (Max 150 words) Working as a part of team Techfest, I have been involved in various social initiatives such as the Anti-Smoking campaign ‘ISMOKE- I Support the Movement tO Kill cancEr’ spanning 12 cities and 50 colleges as a part of Techfest 2014, Internet For All , for digitally empowering 50,000 children in 50 villages in India , and have visited several NGOs in Mumbai for the same. 20. Describe briefly about your hobbies/extracurricular activities/area of interest, which may be relevant for considering your application. (Max 150 words): I have been constantly involved with one student body or another, the reason being I don’t want to miss out any of the invaluable learning opportunity that the campus has to offer. Currently I am a part of the Techfest Team, nominated based on peer reviews, overall academic background and leadership skills, to be one of the core team members involved in the ideation and execution of Techfest. Before that I was the Maintenance Secretary of my hostel during my sophomore year. I have always looked forward for a chance to interact and share ideas with people hailing from different backgrounds and having different perspectives. This is what led me to apply for various international and leadership opportunities and programs including this one. In past I have had the honour of......

Words: 917 - Pages: 4

Free Essay

...Kellie Aosley8 Recent Hedical school &a&ate "CALCULUS FOR THE UTTERLY CONFUSED has proven to be a wonderful review enabling me t o move forward in application of calculus and advanced topics in mathematics. I found it easy t o use and great as a reference for those darker aspects of calculus. I' Aaron Ladeville, Ekyiheeriky Student 'I1am so thankful for CALCULUS FOR THE UTTERLY CONFUSED! I started out Clueless but ended with an All' Erika Dickstein8 0usihess school Student "As a non-traditional student one thing I have learned is the Especially in importance of material supplementary t o texts. calculus it helps to have a second source, especially one as lucid and fun t o read as CALCULUS FOR THE UTTERtY CONFUSED. Anyone, whether you are a math weenie or not, will get something out of this book. With this book, your chances of survival in the calculus jungle are greatly increased.'I Brad &3~ker, Physics Student Other books i the Utterly Conhrsed Series include: n Financial Planning for the Utterly Confrcsed, Fifth Edition Job Hunting for the Utterly Confrcred Physics for the Utterly Confrred CALCULUS FOR THE UTTERLY CONFUSED Robert M. Oman Daniel M. Oman McGraw-Hill New York San Francisco Washington, D.C. Auckland Bogoth Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto Library of Congress Cataloging-in-Publication Data Oman, Robert M. Calculus for the utterly confused / Robert M.......

Words: 53219 - Pages: 213