what does calculus mean?
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Calculus is a central branch of mathematics. The word stems from the nascent development of mathematics: the early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, and the Latin word for "pebble" is "calculus."\n\nCalculus is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.\n\nExamples of typical differential calculus problems include:\n\nfinding the acceleration and velocity of a free-falling body at a particular moment. \nfinding the optimal number of units a company should produce to maximize its profit. \nExamples of integral calculus problems include:\n\nfinding areas and volumes \nfinding the amount of a liquid pumped by a pump with a set power input but varying conditions of pumping losses and pressure \nfinding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.
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integration sign.\nWhen reading a formula, you simply read it "integral of" if there are no boundaries, or "integral from a to b" if there are boundaries a (lower) and b (upper)
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The essence of calculus is the derivative. The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point. Let's use the view of derivatives as tangents to motivate a geometric definition of the derivative
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In fact, the calculus is simple but if you have problems you need to take many classes before it. However, if you have no math clue...well you should start again since the beginning. You can do it, ask for help always and study together with your classmates.
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It depends on what the word "mean" means. :-)\n\nRoughly speaking, under the specified conditions there is a point on the curve between x=a and x=b where the slope of the curve equals the slope of the secant from (a,f(a)) to (b,f(b)).
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In basic calculus, we use the derivative to find the slope of a curve, and the integral to find the area under a curve.  The question is, why are these operations the opposite of each other?\n\nThe quick answer is:  The derivative is used to calculate the rate of change of a function.  And the rate of change of the area under a curve is actually the original function.\n\n\nLet's say you have a simple curve, y=f(x).\n\nThe derivative of the function is gives you the rate of change of that function.  As x increases by 1, how much does y change?  That's also known as the slope.\n\n[And you probably know that the derivative of the derivative is also useful.  That's the rate of change of the slope.  When the slope stops changing (or its rate of change=0), it's at a maximum, minimum, or point of inflection.]\n\nThe same relationship exists for the area under a curve and the function itself.  You probably learned to think of the integral of f(x) as the sum of the thin vertical strips under the curve.  That's the area under the curve.  As you move to the right, how fast does the area grow?  You're essentially adding these vertical strips to the area.  The length of a vertical strip is f(x), or the original function.  So the original function f(x) represents how fast the area grows for any value x.\n\n\nETA: What do I have to do to get selected as best answer?
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No.\n\nIt means that the slope of the curve y = x^2 at a given point is equal to twice the value of x at that point.\n\nThe change in y for an infinitesimally small change in the value of x is equal to twice the value of x at that point.\n\nYour interpretation, "for every change in x there is a change of 2 [in y]", would correspond to a derivative (or slope) of 2, not of 2*x.  The function, y = 2*x + constant would have a derivative dy/dx = 2.
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to get an extra credit, maybe?\n\n---\n\nseriously, I cannot figure out how you can study calculus without knowing limits: even if you only deal with numerical procedures, every iterative formula, or better, EVERY FORMULA (such as those used to find the roots of a non-linear equation, approximated integrals, derivatives and so on) needs a preventive study for convergence conditions: this involves limits!\n\nOne more step back: DERIVATIVE IS A LIMIT ! How can you apply it without knowing what it is?
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Knowing trig makes learning calculus easier.
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"Maths" is a contraction of "mathematics", a short way to say and write it.  It includes all branches of maths, e.g. arithmetic, algebra, geometry, trigonometry, statics, differential and integral calculus, quantum mechanics, etc. As you can see, arithmetic is a subset of mathematics.  Arithmetic deals with the manipulation of real numbers only.
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Yes! Big difference. Arithmetic has to do with simple operations of only numbers involving +, -, /, and x. (adding, subtracting, dividing, and multiplying). Mathematics encompasses EVERY kind of math, from arithmetic to calculus to linear algebra to the stuff they used for the physics to build the atomic bomb.
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tracing a curve simply means drawing the curve on a plane with reference to the coordinate axes by identifying certain special points and characteristics of the given curve like intercepts, domain, extent, asymptotes, symmetry, monotonicity, pts of inflection and so on..\n\n\nany good book on calculus, analytical geometry should help you do this(as tracing involves both the topics)
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algebra is an early form of calculus.\n\nbut what do you think about this\nhttp://answers.yahoo.com/question/index;...
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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.
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I you can express the problems in mathematical relations, yuo can use calculus  everywhere. For businesses you can use differentiation to find sensitivity of for example of profit to  a unit change in cost or sales or production.  you can use integration to find out over all profit or production, etc.
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You could find its first derivative and see when it is greater than zero, indicating a positive slope and therefore increasing - assuming you are in calculus.
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Mathematics- The science of numbers in all their relations and applications. (Math is a general concept including arithmetic, statistics and probability, trig., calculus, and more)\n\nArithmetic- The most elementary branch of mathematics (addition, subtraction, multiplication, division for example)