Real Analyis/Advanced Calculus Questions?
953356
Let f(x) = sin (1/x) and g(x)=-sin (1/x). Neither f nor g have limits at 0, but [x→0]lim f(x) + g(x) is obviously 0.
834713
I can't give you all 30 but I can get you started.\n\nWho discovered Calculus?\nExplain the Fundamental Theorem of Calculus?\nWhat is a derivative?\nWhat is an integral?\nHow is Calculus useful?\nWhere did the name Calculus come from?
961572
Try to find a book on analytic geometry (which should also cover trigonometry), and one that has lots of exercises, which will help you retain all that information.  There used to be a book called Geometry & Trigonometry for Calculus, but it's out of print.  As per the algebra, try to find a cheap Dover Classics book through amazon, they are usually only $10-20.  Also, the following site may help you:\nhttp://ltcconline.net/greenl/courses/152a/152a.htm\nhttp://ltcconline.net/greenl/courses/152b/152b.htm\nhttp://ltcconline.net/greenl/courses/154/154.htm\nhttp://tutorial.math.lamar.edu/AllBrowsers/2413/TrigEquations.asp\nhttp://tutorial.math.lamar.edu/AllBrowsers/2413/TrigFcns.asp\n\nGood luck!\n\nSteve
183373
Try the inside cover of your Calculus book - it usually summarizes the rules for derivatives and some key integrals.
711470
Try here:/\n\nhttp://archives.math.utk.edu/visual.calculus/
101992
Here are some sites that have saved my behind.  :)\n\nhttp://integrals.wolfram.com/index.jsp\n\nhttp://www.calc101.com/webMathematica/integrals.jsp\n\nhttp://mcraefamily.com/MathHelp/CalculusTableOfIntegrals.htm
626773
Calculus has been mostly subsumed by topology, differential geometry and cohomology at the (pure) research level. The language of these topics is much more concise and powerful than that of classical analysis. If you're looking for recent advancements in analysis (the formal name for calculus), these are the fields you should be familiar with. Basically, these fields examine every type of object that one could do analysis on, in a way similar to what one does with basic calculus (continuity, limits, curvature, etc.).\nSee http://xxx.lanl.gov/archive/math for new research in these areas, as well as classical areas.
781528
Definitely any advanced Math courses you can take (Algebra, Calculus, Trigonometry, etc.) I think would be helpful, especially Calculus.
460400
You would need to know how to integrate (that is, find anti-derivatives). The proceedure forthis type of problem can usually be understood after first semester calculus. The specific integrations may need some second semester calculus.
359311
I am studying for the AP Calclus test right now and I am as ready as I will ever be.  It is my language test (AP Spanish) that I feel unprepared for.  I just suggested this to someone else for AP Calc so I will tell you too, study:\n\nsolids of rotation (disc, washer, and shell), the fundamental thereom of Calculus (what integral means), U-substitution, derivative rules, Riemann sums, speed, linearization (finding the slope of the tangent line), volume of known cross sections, concavity and inflection points, the area between two curves, differentiability and continuity, local and global extrema (critical points and end points), implicit differentiation equations, trignometric derivatives, the rule of exponential growth (like volume increasing at a rate proportional to the radius), average value of a function, optimization, and related rates. \n\nI know that is a lot but I have taken 5 complete practice AP tests (former tests) in class since February and all of these concepts were reccuring.
540612
give me ten points if u need further help just mail to me.\n\nhttp://tutorial.math.lamar.edu/AllBrowsers/2413/2413.asp\n\nhttp://www.calculus.org/\n\nhttp://www.math.ucdavis.edu/~mikew/free_calc.pdf\n\nhttp://www.math.gatech.edu/~cain/notes/calculus.html\n\nhttp://www.exambot.com/cgi/topic/list.cgi/math/difc?class=hlink
645
The farthest I went was Calculus II in college.  Do I use advanced calculus in my everyday life?  No.  \n\nHowever, it's not the idea of using it in everyday life, it's the problem solving skills you gain that make you smarter.  It helps to show you there are many ways to approach problems and helps you choose the best way to try solving them.  Don't give up on difficult subjects like these in school.  While you may not use the concepts day to day, you'll use problems solving skills every day for the rest of your life.
392380
All kinds of simple, easy calculus examples in real life (especially engineering!).  These depend on the level of math knowledge, but for University Calc. II:\n\nOptimization: (i.e. give a box with a volume, find minimum surface area) or (here's a certain amount of fencing, make the largest enclosure you can).  (Lagrangian Multipliers? did I even spell that right?  We looked at those when there are a lot of constraints on the problem (i.e. relationship between box dimensions must follow .....).\n\nForces: for example, average fluid pressure on a dam, given a function of distributed force, or fluid pressure on a submerged object. (Can be done in single or multiple integrals).\n\nRelated Rates:  i.e. two cars approach at right angles, different speeds, when will they meet.  Or, dropping a ball near a light source, find speed of shadow as function of angle made with light source, distance from ground, etc.  Differetial calculus example.\n\nArea and Volume: Double and triple integrals to find the volumes and areas of shapes. (Or single integrals, volumes of revolution, areas from curve to axis, if multi-variable calculus not covered).\n\nCurve Fitting: really good real-life use, take a set of data points from an experiment, select a curve type (i.e. quadratic, cubic, straight line, logarithmic, etc) and use minimization to get the best curve fit (set up an equation for the residuals, sum of (function) - (data point), and take derivatives with respect to each unknown coefficient in the function, set all derivatives equal to zero, solve simulatneously for curve coefficients. Now we can predict the outcome of the experiment at intermediate values, (as long as the curve fit is good).\n\nCentre of Mass, Centroids, etc: Find the balancing point on certain objects or groups of objects using integration. Can be single or multiple integrals, depending on complexity of shape.\n\nFields:  i.e. graviational fields, electrical fields, etc.  Or make up some fields.  Integration to find work required by a particle to traverse a path through some field.  Conservative and non-conservative fields.  Can use as an example of energy needed to move satellites along paths (equations) in space near earth's gravity, an electron through an electrical field, etc.  I guess some of these examples the field is conservative and it becomes kinda trivial if you work with end points, but don't have to.\n\nThese are some of the applications we used in our Calculus II-type course.  The hardest part is always setting the problem up, not solving, (which makes for good application problems I guess).  If multi-variable calculus isn't covered yet, then some of these examples would be kinda rough (i.e. fields).  Anyway, hope these are useful. \n\nCheers,
57176
http://www.calculus.org/
125046
I have a bit of calc links from when I took the AP exams.\nhttp://www.jimmyr.com/education.php\n\nunder the section calculus. those sites were really useful.
12471
checkout these links\nhttp://archive.devx.com/dbzone/articles/sf0701/sf0701-1.asp\n\nhttp://www.ca.com/products/jasmine/analyst/idc/14821Eat.htm\n\nhttp://www.w3.org/Conferences/WWW4/Papers2/282/\n\ncheers\nSunny
657050
1) f'(x) = 40x^4+6x^2+4\nTo find local max's and min's, set this equal to zero, but you will see that all solutions will be imaginary, so there are no local max's and min's on the real line.\n\nf''(x) = 160x^3+12x\nTo find the points of inflect, set this equal to zer, but you will see that the only place where there is an inflection is a x = 0.\n\nSo what have we learned?  f(x) is a strictly increasing function, meaning tha there could only be one real root.\n\n2. Let u = 1+t and use substituion.