Calculus

Question: Calculus..............................… Every time I look at calculus I keep asking the same question. Algebra1, Geometry, Algebra2, pre calculus can be learned in one year at this pace calculus should be a five year long subject how the hell can they learn it in one year, me I love math and did well in all those prior subjects but calculus doesn't seem to go next I mean pre calculus one year next year calculus it should come several years later.

Answer: That's very true: calculus can't be finished in one year. I takes one year to even understand the fundamentals of calculus, i.e., how limits and derivatives and all those things work and stuff. The best way to approach calculus is to learn it on your own before they actually teach it in school. I haven't even done pre-calculus in school yet, but i finished learning calculus on my own. Learning on your own before the semester begins helps you to really understand what your instructors are teaching you and it will all get in your brain that much faster. Hope this helps. EDIT : No, I'm not talking about differential equations, I'm talking about the basic fundamentals of calculus, like limits and derivatives. Actually, if you undersand these fundamentals, the more advanced concepts are pretty easy. When I say 'understand', i mean REALLY understand it, you know, get that 'Aha!' moment. That isn't easy to come by. I realized that I never really understood second derivatives until I learned about the power series. However, after I learned about second derivatives, the Taylor and Maclaurin series became a cinch and (with a little fundamental vector algebra knowledge), the Fourier series made sense too. So, when I say 'understand', I mean understand to a degee of perfection.

Question: calculus ......................? need any calculus question and correct answer. thanks

Answer: Here's a good calculus question for you: Find all local extrema and concavity of f(x)=x^2+5x-3. Find first derivative: 2x+5 Find critical numbers: -5/2 Determine where function is increasing: x is decreasing from -infinity to -5/2, increasing from -5/2 to infinity, so according to that, there is a local minimum. Find local minimum: Replace -5/2 into original equation:(-5/2)^2 + 5(-5/2) + 3 25/4 + 25/2 + 3 25/4 + 50/4 + 12/4 = 87/4 Local minimum at (-5/2,87/4) Find concavity: Find second derivative: 2 Find critical numbers: 2 Determine if concave up or down: Concave upward on all intervals. There ya go Miss Kristin

Question: CALCULUS!!!!!!!!!!!? What would you say is that hardest thing to do in Calculus?

Answer: well if you're talking about calc 1 then i would have to say going from differentiating to integrating...neither are really hard concepts it just gets confusing sometimes because they are basically the opposite of each other...just be careful

Question: ???CAlculus??? Find all Critical numbers of the function f(x)=(9-x^2)^3/5

Answer: that means to find all the points where the first derivative of that function is 0. f '(x) = (3/5)[(9-x^2)^(-2/5)](-2x) simplifies: f '(x) = [-6x]/[5(9-x^2)^(2/5) if we set that equal to 0, then the top of the fraction is all that we need to be 0 so -6x=0 x = 0 is our critical point

Question: CaLCULUS!!? evaluate lim (ln(x^50)) / x^100 x->infinity show full solution please

Answer: This is a L'Hopital's Rule question. You can see that normal evaluation gives you ∞/∞ , an indeterminate form. So first do something that'll make this easier: change ln(x^50) to 50lnx (logarithmic rules allow you to do this). You have the limit of 50lnx / x^100 . Take the derivative of both the top and the bottom (NOT the whole expression): [50/x] / [100x^99] = 1/2x^100 . The limit of this expression as x goes to ∞ is more clearly 0. So your answer is 0.

Question: How different is differential calculus to integral calculus? How about in terms of difficulty? I'm liking my half-year (one semester) calculus class a lot, that I'm considering taking the second-half (second semester). I originally intended to only take one semester of calculus to fulfill my math requirement, but I might want to take the other half for an elective. For first semester, we learn derivatives. Second semester is integral. How different is differential calculus to integral calculus? And how different are they in terms of difficulty (in comparison to each other)? Thank you.

Answer: Well, computationally, they're worlds apart. Differential calculus is used to basically take a function and target a specific point in that function. Integral calculus is used as almost the opposite: you take a function and you measure the area under it's curves. Actually, integrals are also known as the "anti-derivative", so yeah! One does need to know the derivatives to a fault... or, literally speaking, backwards! If f(x) = 1, then f'(x) = 0 On the other hand: if f(x) = 1, then ∫f(x) dx = ∫(1) dx = x + C Likewise: If f(x) = sin x, then f'(x) = cos x If f(x) = sin x, the ∫f(x) dx = ∫(sin x)dx = -cos x + C It's fun and has more real-world applications, in my opinion. Good luck!

Question: How much calculus should I take before taking calculus based physics? I am in college right now. For my sophomore year I will be taking second semester chemistry and first semester of calculus based physics. After this semester I would be done with one year of calculus. Is that sufficient for physics?

Answer: First term calculus based physics does involve integration, but they're very basic integrals nothing like you would see in calc 2, where you learn integration methods. Mostly you'll use derivatives as far as calculus is concerned. I took physics I after calc I and I did fine.

Question: What is the difference between Business Calculus and regular Calculus 1? I have heard that business calculus just concentrates on the application of calculus to solve business problems and that there is no geometry or trigonometry involved. I have also heard that business calculus is a "watered down version" of calculus 1.

Answer: use perhaps the Riemann's dzeta function

Question: How important is calculus in high school? I am a high school senior going into mechanical engineering. I am better then most at physics ( in ap physics 2) but about average at calculus ( im in advanced calculus 1) is one more important then the other and will i be behind other engineering majors in calculus?

Answer: Considering that you are planning on entering mechanical engineering I would judge that you need the calculus more than the physics but mechanical engineering majors have to have physics also. You will probably use the calculus in your advanced courses more than the physics. Do not worry too much about whether you will be behind -- you still have many more advanced math courses ahead of you.

Question: What is calculus and differential equations and how are they used? I graduated with a degree in math. I took four semesters of calculus, plus differential equations. I can do the math with A's, but I still have no idea exactly what calculus and differential equations ARE and why you would use them.

Answer: Calculus is the mathematics of infinitesimal change. Since you're familiar with calculus, for example, "dy/dx" means the instantaneous rate of change in y with respect to the instantaneous rate of change in x. Integrals, or "anti-derivatives" are sums of these infinitesimal parts. With them, you can find the areas under different curves and such. Differential equations are very useful for when you know quantities that are changing, or you're looking to solve something that's "in flux." I hope this helps.

Question: What makes calculus a class with a high failure rate? According to my professor, calculus is a class with a high failure rate and they have found that it's because students coming from high school may not have all the pre-calculus knowledge required to do well in calculus. So we're all required to attend a pre-calculus workshop 3 times a week for two months. But I hear from my friends that pre-cal isn't very related to calculus. So what is it, really that causes a high rate of failure? Curious.

Answer: I think a lot of people fail calculus because they are or were average in all the math previous math classes and since calculus requires all maths from simple arthmetic to algebra to pre cal and people tend to forget some of the things used before and it's hard to learn since a lot of students have to review previous topics but mainly calculus 1 is algebra intensive and there is some super dreadful word problems and calculus 2 is mainly theory so it's not that hard and 3rd semester and 4th semester is just super hard But if you are good in math calculus will be simple

Question: What is a good Multivariable calculus textbook at the university level? Right now, my multivariable calculus class uses "Vector Calculus" by Marsden and Tromba but I really dislike how this textbook is written. It is obscure, is not good at explaining it's examples and often times I feel like it isn't comprehensive enough. Could you guys recommend to me a very good Multivariable Calculus textbook that I could read and then understand this material? Thanks in advance!

Answer: Agree with phoenix. Can't go wrong with Stewart! Here is some library link. http://www.worldcat.org/oclc/44837382&re…

Question: What is the relationship between Calculus and Physics? How is the topic of physics and calculus related, and how do these topics depend on each other. For example, acceleration is taught in calculus even though it is a pure physics problem. What are some other instances in which these topics depend on each other? what topics? How exactly are they related? I've noticed over several years, that even excellent math students find calculus and physics difficult, why do many find these topics difficult? Is it the mathematics or concepts that are hard to understand? I thank all in advance. Thanks.

Answer: It just so happens in our universe that the universe can be explained and understood in terms of mathematics. Why this should be the case, nobody knows- that is a meta-physical question. Perhaps we humans need something like mathematics to help us understand the universe, we have used mathematics to analyse, axplain and understand the universe. Or maybe there is a more fundamental connection. Maybe "Mother Nature" is a mathematician... Acceleration doesn't need to be taught in calculus. A calculus course could be completely abstract, without reference to the real world. But, calculus has found an extremely wide range of application, so it makes sense to bring in the applications in a calculus course, not least because those taking the course may want to apply to real world problems (physicists, engineers, even business men), but it also helps heuristically if it relates to the real world, things that are tangible and 'knowable'. That is to say, calculus does not depend on physics. Calculus to be completely abstract. But it is quite unlikely that physics would have gotten far without calculus. Just about every branch of physics can be dealt with within the framework of calculus- dynamics, kinematics, hydraulics...- you name it. Some topics in physics would even be impossible without calculus, such as variable acceleration. Even in quantum mechanics, where (almost) everything is discrete, calculus plays an important role. But, one could say that certain physics problems which required an analysis with calculus, sort of spurred on the developement of calculus, in a similar way that engineering problems pushed physics forward (think Fourier Series etc.). Why does calculus find so much application in physics? Calculus basically deals with infinitesimal changes- changes that are not zero, but smaller than any imaginable real number. In physics (reality) the universe operates with infinitesimal changes. So calculus (specifically, infinitesimal calculus) works splenidly with the real world where things can be analysed infinitesimally. And such infinitesimal analyses covers the (usual) situation where the quantity in question is not constant, or not even changing at a constant rate, which would not be possible without calculus. And that would explain why calculus and physics are difficult. Calculus requires thinking about infinitesimal changes, which sound quite contradictory and mind-boggling. Calculus is unlike any other branch in mathematics. Also, physics requires a sort of "visualisation" and intuition about physical reality. One must also remember that the topics covered in one physics or calculus course (at university) may have taken thinkers and scientists centuries, and even millenia, to come to grips with, and all that thought is condensed into a semester or one year. It makes you think....

Question: What is the difference between calculus and regular math? In about a paragraph can you explain how calculus is different from regular math? Why do we need to take about a year of pre calculus to prepare for calculus?

Answer: Calculus deals with slopes of functions at any given point(derivatives), as well as area under the curve (integrals). Calculus is usually broken into 4 years. Calc 1 (using limits to find derivatives, other ways of finding derivatives, fundamental theorem(s) of calculus, applications of integrals and derivatives) Calc 2 (more ways to integrate. integration and derivatives of polar functions) Calc 3 (Multi-variable calculus) Calc 4 (Differential equations) Pre calculus is a rigorous course to prepare students for the abstract thinking needed to succeed in Calculus, as well as strengthen their foundation on commonly used mathematical skills.

Question: Calculus Teachers: How much review do you go over in the beginning of the semester? I will be teaching Calculus I with Analytic Geometry this semester (College Level). I am planning on spending three to four class periods reviewing algebra concepts. Coming off a summer break, I think it's a good idea to review.

Answer: I would say none if it's at the college level. They can do there own review. But to be nice I would do a class period doing some algebra review.

Question: Is the best way to learn calculus through self study through a traditional book or an applied calculus book? I remember reading that somewhere. I already have been using my old precalculus book and a Calculus for Dummies book but I need something with a quicker pace that I can use until I purchase a TV for the Calculus DVDs.

Answer: I taught myself calculus in highschool and in one year scored a 5 on the AP test. I would avoid using any sort of DVD's unless you are stuck in the book without any other help. Second, I would definitely use a traditional book. If you want to learn a little slower, but with a better understanding I would search for a college level Calculus book. If you do not feel comfortable with that then find an AP level highschool calculus book. Calculus for Dummies is not worth the money you paid for it. It will give you a "bare bones" understanding of calculus which will not be enough if you plan on using calculus in the future for a degree or in a job environment.

Question: Is it ok to take Physics (Calculus based) with a background of only College Algebra and Trigonometry? Hi guys, I just wanted to seek a little bit of your advice. I have not taken Pre-Calculus or Calculus before. But I have taken College Algebra and Trigonometry. I am planning to take Physics I (Introductory Physics I) which has Calculus I as a Co-requisite. Do you think I'll be able to handle and pass Physics I with my background? Thanks!

Answer: Depends on the difficulty of the University. If you're at MIT, University of Michigan, Virginia Tech or another top ranked science university then i would never go into a class under prepared. If it's in a community college there should be enough people that don't know what's going on anyway that you can get away with not knowing all of the calculus background for a calc based physics class

Question: How to use calculus in order to determine number of skittles in cylinder? I'm doing a calculus fair project, and I need to know how to start, what measurements to take, etc. I'm not sure as to how to take the volume of a skittle, then the volume of the cylinder using calculus. The main idea is to predict how many skittles will fit in a cylinder based on volume. Any ideas will be helpful. Thanks!

Answer: It will take some calculating, but that's not quite the same as calculus. I'd suggest finding the "density" of skittles. Density would be the number of skittles / known volume then convert that to a volume easier to work with. For example, fill a cup with skittles, then count them. I've no idea what you would get, but lets say it takes 500 to fill a cup. 1 cup = 14.4375 cubic inches 500 / 14.4375 = 34.63 skittles / cubic inch. Density = 34.63 skittles / cubic inch From that, you can estimate how many skittles can fit in any volume simply by calculating the volume in cubic inches and multiplying by 34.63 A box 1 foot, by 1 foot, by 1 foot = 12 * 12 * 12 cubic inches 1728 * 34.63 = 20736 skittles / cubic foot.

Question: How do you study calculus and retain the information you learn? I'm taking my second calculus class this semester and I can't seem to remember anything from the first one, or to retain anything new. Math has never been my strongest subject, but I've always managed to do fairly well. I can't seem to do even that much now. How do you study calculus? How do you retain the information from one math class to another, and when using it in other disciplines?

Answer: Hello. This is a very common question, and actually, in my opinion, it is rarely ever addressed properly. The problem is that people try to study math like they would a history class. They try to memorize all of the formulas letter for letter and don't give it a second thought. This is obviously wrong (although, admittedly, this is a bad way to study history, as well) - math is NOT memorization - it is about problem solving. You take some concepts that you know and apply them generally to NEW problems and ideas. So, you should understand the concepts behind what you are doing in class - you must understand what your formulas actually mean and decide how to apply them. I'd really like to direct you to "Paul's Online Notes" (Paul, by the way, is a college professor). He has a little page on "How to Study Math". His discussion may be of more value to you than mine. http://tutorial.math.lamar.edu/Extras/St… Good luck to you.

Question: How difficult are finite mathematics and basic calculus? I recently changed my major. As part of this change, I have to take two extra math classes - finite mathematics and basic calculus. I made an "A" in college algebra, but that was like a year ago, so I'll have to review some. How hard are these two classes? How much of college algebra do these two classes contain? Does basic calculus have the same material as calculus 1?

Answer: i dont think your gonna have a problem with it, i mean if its just basic stuff and u got an A in college algebra..ur good to go. good luck!