What is Calculus 1: Definition and 96 Discussions

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine – see Calculus (medicine)). Because such pebbles were used for counting (or measuring) a distance travelled by transportation devices in use in ancient Rome, the meaning of the word has evolved and today usually means a method of computation. It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.

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  1. hgducharme

    Can I Self-Teach Calculus 1 to Enroll in a Physics Course?

    Ok so long story short, I need to enroll into a physics course that requires you to have taken Calculus 1. I am going to try and enroll, and hope that my enrollment office doesn't check my course history. ASSUMING hypothetically that I get the option to actually enroll and don't get denied...
  2. iwantcalculus

    Trying to self-learn calculus but stuck on this idea

    So I started with limits and everything went well, and then into derivatives, and a problem started. First I know how to find the derivative of basic things using like ( limit definition of derivative) or (rules for derivatives) or ( product rule/ quotient rule/ chain rule)... My problem...
  3. C

    Solve f(x) Diff. at x=2: Find a,b,c Values

    Homework Statement The problem is: f(x) = {ax^2 - b / (x - 2), x < 2 1/4(x^2) - 3c, x >= 2 If f is differentiable at x=2, what are the values of a, b, and c? In case it is hard to see, I have provided an image 2. Homework Equations I know that the limit definition of a...
  4. E

    Is a B in Calculus 1 and 2 the end for me?

    Hi all, So I'm pretty devastated(and I'm to be blamed). I'm a first year cs and math major. So the thing is my math course is a full year course with 5 class tests and 2 finals(worth 2/3 of the final mark) Slacking off and poor time management gave me the privilege of failing all my class...
  5. S

    Calculus 1 and 2 regards to Civil Engineering

    Hello Physics Forum, I am an aspiring civil engineer and I just stumbled across this website tonight. I am just now taking calc 2 and have pretty much started off on the wrong foot. This class is already a headache and we have just covered the first quarter of the class. I expect it to get...
  6. A

    Problem books of applications of calculus 1

    Hi there, everyone! I'm sure this question has been asked many times before, but I did not really find any similar posts, so I hope you guys will bear with me! I am teaching myself what could be categorized as Calculus 1, using Adams' "Calculus: A Complete Course" along with "Schaum's 3000...
  7. C

    Calculus 1 Homework problem - Find limit without L'Hospital's Rule

    Homework Statement Lim ( 5+6x2)/(√(x3)) + 2x2 +1) x->∞ Homework Equations not allowed to use lhopitals rule The Attempt at a Solution first, i divided by x2, which yielded (5/(x2) + 6 + √(x)) / (2 + 1/x2 ) then i assumed that thelim x--> infi of 5/x2 = 0, lim x-->...
  8. A

    Advice needed on how to handle 3.5 week calculus 1 course

    I'm hoping you guys/girls can give me some advice / techniques to getting a good grade in a 3.5 week summer calculus 1 course. I just finished the first week today, and there are about 3 more. There is a test each Friday, and I took the first one that was worth 12.5% today. I did bad. The...
  9. T

    How to get better at optimization calculus 1 problems

    Im having trouble starting the harder optimization problems in stewarts calculus (calculus 1). I noticed one of my major problems is not knowing how the picture of the optimized problem looks like. My test is only going to contain one optimization problem. So I am not worried about failing...
  10. T

    Not sure to take Methods of Discrete Mathematics after Calculus 1

    I am a math major and I need to take Methods of Discrete Mathematics. What is methods of discrete mathematics? Should I take it after My calculus series( including linear/ diff. equations)? Is it easy enough to take with Calculus 2? Thanks
  11. H

    Calculus 1 Differentiation Problem: Chain Rule with Binomial Theorem Application

    I'm not entirely sure if this belongs in homework or elsewhere -- I'm self-teaching working through a basic calculus text, so it's not homework per se. In any case it's a simple differentiation problem wherein I am supposed to differentiate: f(x) = x(3x-9)^3 f'(x) = 3x(3)(3x-9)^2 Applying...
  12. T

    Schools Question about Calculus 1 in university.

    My question is what does Calculus 1 consist of in college (community college which is not that proof heavy). I have the Morris Kline book which I am self learning from and so far so good. I finally understood how vectors work in reference to an object m sliding down a slope which is...
  13. I

    Calculus 1 relative rates question

    Homework Statement An airplane flies at an altitude of 8 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°, and θ = 80°. The Attempt...
  14. S

    Calculus 1 Help: Solving Weight Formula for Distance

    Okay I had a calculus test and we got it back and I got this question wrong. I tried it again but I can't figure it out. The weight, w, in kg of an object is inversely proportional to the square of the distance, r, in km, from the center of the earth. Assume a stone of the ground has weight...
  15. A

    Physics 1 harder than Calculus 1?

    Hello, I've been around the forums before, but I finally decided to create an account to post things. :) I'm currently a sophomore in college majoring in physics. At my school physics 1 and calculus 1 are a co-requisite not a prerequisite, meaning I can take physics 1 and calculus 1...
  16. M

    Understanding differentials in Calculus 1?

    I'm taking a short Calculus session this summer and the teacher zooms through things. I still don't fully understand differentials. I know that derivative give you the slope of a function at any point. And I know that dy is a small change in y and dx is a small change in x and how they can be...
  17. A

    Would it harm my later in life to take calculus 1 online?

    So this summer I was planning to take calc 1 at a school, but they canceled it. Very aggravating. But I can take the course online somewhere, so will it hurt me later on to take it online? Also does anyone know of good accredited places that I could take calc 1? I was thinking BYU or I don't...
  18. T

    Quick Calculus 1 Homework Help Needed: Final Exam Prep

    Homework Statement The Attempt at a Solution I figured out #11, could use help with the other questions. I have a final tomorrow in the morning and my professor gave us a few questions to try out so help would be appreciated. For #8 I'm not sure how to draw the second...
  19. W

    Taking Calculus 1 again. I don't understand algebra. Should I give up?

    maybe I posted this in the wrong place. I signed up for an online university calculus course. I forgot most of algabra. Should I drop it and try to learn my stuff first? Can I learn it in 5 weeks? They give you about 6 months to complete the online course. I figure I can dedicate 15-20 hrs a...
  20. T

    What are some creative extra credit ideas for Calculus 1?

    Hello everyone, this is my first post so if I am doing something wrong let me know. My first year college calculus professor has slipped a little cookie into her syllabus that says the following. "Extra credit is a demonstration of excellence and mastery of skill taught in this course in a...
  21. B

    Reviewing Topics for Calculus 1

    I'm currently taking Calculus with Analytical Geometry and I need to do some expedited review of the Trig and the algebra pertinent to the course. Does anyone have a definitive list of topics one should cover prior to learning calculus material? Any tips( P.S.- I want an "A" in this course)?
  22. K

    Calculus 1 Integration Problem

    Homework Statement Calc I problem, so need to solve by calc 1 methods. ∫ (x-1)(x+1)^11 dx Homework Equations The Attempt at a Solution ∫ (x-1)(x+1)^11 dx U = x+1 dU = dx x-1 = x+1-2 = U-2 =∫ (U-2)U^11 dU =∫ U^12 dU - 2∫ U^11 dU =(1/13)U^13 - (1/6)U^12 =(1/13)(x+1)^13 - (1/6)(X+1)^12 ∫...
  23. C

    Schools AP Calculus(HS) vs. Calculus 1 (College)

    Hey, I am taking AP Calculus next year in High School. Is it the same thing as Calculus 1 for college? Reason why I ask I am looking to learn all of the material in advance.. Would this be a solid guide to follow -...
  24. ME_student

    Calculus 1 (I'm taking the class in a week.)

    I am finally getting my feet wet, actually taking math courses that apply to my degree. Anyone have any suggestion what I should be studying before I take the class? I have borrowed a book from a local library called "Calculus Essentials for Dummies." I have a friend who is in calc 3, I...
  25. D

    Calculus 1: Finding the maxima and minima of the function 1-x^(2/3)

    Homework Statement I am given the problem "A function is defined by f(x) = 1-x^(2/3). a. find the minima and maxima of the function. State whether they are relative or absolute. b. graph the function." Homework Equations I found the derivative and set it equal to zero. y' =...
  26. I

    I got a B+ in Calculus 1, should I reconsider being a mathematician?

    I go to a top 10 math school in the US and just received a B+ in Calculus 1 (the final was ridiculous!). Should I reconsider being a math major? I enjoyed the course considerably, but I feel that all math majors would breeze though it with an A. Any thoughts? Thanks.
  27. C

    How can I improve my understanding of Calculus 1 by tackling tougher problems?

    Hi All: I am taking Calc 1 at a community college and we are using Calculus by James Stewart 7th edition. I am able to do homework problems that are assigned to us which are only a small subset of problems from end of the chapter exercises. However, we are not doing any of the remaining...
  28. R

    First time exposed to Calculus 1 and I'm not doing so well. I'm in the

    first time exposed to Calculus 1 and I'm not doing so well. I'm in the Mechanical Engineering major and I keep getting discouraged that maybe Engineering isn't the right choice for me. any suggestions?
  29. D

    Calculus 1 Solving logarithmic equation

    Solve for b, f(x)=b^x Here is where I am so far lny=lnb^x lny=xlnb^x y'/y= lnb e^y'/y= e^lnb b= e^y'/y My question is, can I simplify the exponent y'/y any further, or is my answer good here? Thank you
  30. J

    Calculus 1: Easier the Second Time Around? Opinions Wanted!

    Taken previously? Right now does a calculus 1 class , seem easy to you, compared to when you first took it? Usually when you take math classes they seems kind of daunting at first and then when you do math beyond that what seemed kind of perplexing at first becomes super easy? Opinions?
  31. M

    Solving a first order differential equation (calculus 1)

    Homework Statement dy/dx=y-e-x Homework Equations none The Attempt at a Solution According to Wolfram Alpha the solution is y = cex+.5e-x . I tried multiple approaches, but I cannot obtain this answer. I can't figure out what step 1 is. I tried factoring out e-x from the right...
  32. T

    Arctan absolute value problem, calculus 1

    Homework Statement prove |arctan(x)-arctan(y)| \leq |x-y| The Attempt at a Solution I tried separating cases: 1. both x and y are in the same quadrant; 2. x and y are not in the same quadrant; 3. x and y are zero (trivial); 4. either x or y is zero. Now, i can see why each of these is...
  33. mathyou9

    Precalculus review or Calculus 1

    Irrelevant context for anyone interested (feel free to skip this blue paragraph): I've always been a geeky, scientific nerd-type. But I've only been sort of a dilettante with all things science (i.e., well above the 50th percentile amongst my peers, but no area of expertise, by any means.)...
  34. Mentallic

    Integrating Double Integrals: A Calculus 1 Challenge

    Homework Statement find \int\int_D sin\left(\frac{y}{x}\right)dA bounded by x=0, y=\pi, x=y^2The Attempt at a Solution I've only studied calculus 1, this problem is for my friend. I did read up briefly on double integrals however and this is why I'm stuck: From the limits and where the graphs...
  35. A

    Basic calculus 1 question: What is the defining formula of sinΘ?

    Homework Statement Q) Derive the dereitvative of sinΘ using the definition of differentiation. I am in Calculus 3, and I used to know how to work this problem very well! :) I just don't remember lol - I just need a little help I guess! :) Homework Equations lim [f(x+h) -...
  36. W

    How Does the Mean Value Theorem Apply to Finding the Slope on an Interval?

    Homework Statement Consider the function f(x)=2x^3−12x^2−72x+6 on the interval [−4,7] . Find the average or mean slope of the function on this interval. Homework Equations MEAN VALUE THEOREM f'(c) = \frac{f(b)-f(a)}{b-a} The Attempt at a Solution When I set this problem up in...
  37. D

    Proof: F(1/x) Gets Negative Values for Odd Polynomials

    given F(x)=\sumakxk (0<k<n) a polynomial function of factor n while n is an odd number and an<0 , prove that : F(1/x) gets negative values for a small enough positive x
  38. W

    Calculus 1 finding absolute max and min

    A University of Rochester student decided to depart from Earth after his graduation to find work on Mars. Before building a shuttle, he conducted careful calculations. A model for the velocity of the shuttle, from liftoff at t = 0 s until the solid rocket boosters were jettisoned at t = 79.2 s...
  39. S

    Calculus 1 Book: "Intuitive and Physical Approach" - Have You Used It?

    I have order: Calculus an Intuitive and Physical Approach, and It is due to arrive tomorrow. I had wanted to buy it because I wanted to learn some physics along with the calculus however now I am starting to think that maybe it was a bad choice since I was thinking that it wasn't a very good...
  40. R

    Optimizing Cone-Shaped Drinking Cup Design

    Homework Statement A cone-shaped paper drinking cup is to be made to hole 27 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. Homework Equations S = \pi r2 \sqrt{r2+h2} The Attempt at a Solution I'm having trouble getting off my...
  41. rocomath

    Calculus 1: Solving Limits Without L'Hopital

    So I was helping this person the other day, and this problem made me pretty mad. \lim_{x\rightarrow\frac{\pi}{9}}\left(\frac{\sin x}{x-\frac{\pi}{9}}\right) First, I added and subtracted pi/9. I regrouped the angle so that it was sin[(x-pi/9)+pi/9] and expanded it, but that didn't help at...
  42. rocomath

    Check , Volumes for Calculus 1

    Check please, Volumes for Calculus 1 Been a while since I've done these type of problems, check please! http://img70.imageshack.us/img70/3558/volumes1iy0.jpg" http://img70.imageshack.us/img70/6768/volumes2aa9.jpg" 1. Find the volume of the solid generated by revolving the region about the...
  43. T

    I have the possibility of taking Calculus 1 and Discrete Math next semester.

    From the people I've spoken to, the general consensus is to take the class in separate semesters if possible. What do you guys recommend? I have 3 semesters left before I finish my AA and I want to get as many math courses in as possible... Thanks.
  44. S

    Can f(x) ever be greater than e^x?

    we have f(0)=1, f '(x)>=f(x) we shall prove f(x)>e^x for every x>=0 thanx to the solvers
  45. G

    Calculus 1 (limits, VA and constants)

    Im in calculus 1 and need some help Question: Find the vertical asymptotes for… F(x) = x^3 + 8 / x^2 –4 I got a va of –2 F(x) = 2x/ sin2x I got a va of 1 Find the limit Lim tan^2 2x/ x^2 x-0 I got 4 as my answer Lim x^2 –4 / (x + 2 )^2 x- (-2) I got –4/0 = no limit...
  46. F

    Having a problem with a fairly early Physics with Calculus 1 problem

    Hi all, been a while since I posted here needing homework help but it's a new semester and I'm already stumped (much to my shame :shy: ) Anyway, I am presented with the following problem: Gold, which has a mass of 19.32 g for each cubic centimeter of volume, is the most ductile metal and can...
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