what is extrapolation?
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Extrapolation is a process of logical induction.  You take a trend from observations, and assume a trend holds in order to predict the outcome of a hypothetical observation.
618425
What you do with extra-polation is assuming that the data is developping along a linear function. So you'll be searching for the function y = c * x where the sum of (your found y-data minus the y-value from the function) is at its minimum.\nSay you found:\n(x,y) = (7,3); (23,8); (26,7); (30,11)\n\nThe function values for these x-values would be:\n(x,y) = (7,7c); (23,23c); (26,26c); (30,30c)\n\nAnd the sum of the differences:\nT = (3-7c) + (8-23c) + (7-26c) + (11-30c) =>\nT = 29 - 86c\n\nT is at its minimum as T = 0, so:\n29 - 86c = 0 =>\nc = 29/86\n\nSo the line you would be looking for is y = 29/86 * x
1152442
Filmarity of simultude
984612
heres a detailed answer and definition, good luck
770990
I don't understand your statement of the problem.  It sounds like it might be an exercise in integral calculus, in which you integrate the expression at hand, evaluate the resulting function at the two limits, and take the difference.
318235
Integration is the calculation of the area under a curve and the inverse of integration - differentiation is the calcutation of the gradient of a curve
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The totality of circumstances surrounding an organism or group of organisms, especially the combination of external physical conditions that affect and influence the growth, development, and survival of organisms.
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the external angle\n\ni hope that this helps
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in this case "extra" means "beyond" as in "beyond ordinary". it is greater than ordinary.
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Anytime you have a problem that is continuous, as opposed to discrete, you will need to use either integration or differentiation to characterize the solution.  That means to say that every problem that involves time in one way or another will necessitate the use of calculus to find an answer at some instant in time.  If the problem is such that you can approximate the answer, then you can discretize the parameters as small slices of time and come up with an approximate answer - without using calculus.
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a spline is a function that helps with smoothing data.  Cubic splines are the most popular. It basically fits a cubic polynomial with the given input data.  You could search on Yahoo! search for cubic splines for more information.
354201
I don't even know what that means. Sorry. A little more details would be nice. Thanks!
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Infinitesimally small.\n\nZero.
353190
When estimating some value, there will always be an error due to innaccuracies and inconsistencies in the measurement and calculation stages.\n\nThe size of the error explains the range of possible values that the actual measurement falls in. So a measurement of 30 ± 2 means the range of possible values is 28 to 32.\n\nIf the error of the estimate becomes larger than the estimate, then the estimate is useless because it hasn't narrowed down the range of possible values.\n\n30 ± 30 means a range from 0 to 60. This effectively means the value could be anything from nothing to a large amount, which is not a useful estimation of the value.
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Newton advanced it as an axiom, by virtue of which it wouldn't be "proven", only tested (the resulting predictions tested.) If I say "suppose I assume a space where all parallel lines converge", I don't "prove" my assumption - it's an assumption. You work outward from it and see what you get. If what you get is impossible (or wrong), it was a bad assumption.
234940
Does the following page help ? http://en.wikipedia.org/wiki/Hermite_interpolation . Compare with your notes.
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In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points.\n\nIn engineering and science one often has a number of data points, as obtained by sampling or some experiment, and tries to construct a function which closely fits those data points. This is called curve fitting. Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points.\n\nA different problem which is closely related to interpolation is the approximation of a complicated function by a simple function. Suppose we know the function but it is too complex to evaluate efficiently. Then we could pick a few known data points from the complicated function, creating a lookup table, and try to interpolate those data points to construct a simpler function. Of course when using the simple function to calculate new data points we usually do not receive the same result as when using the original function, but depending on the problem domain and the interpolation method used the gain in simplicity might offset the error.\n\nIt should be mentioned that there is another very different kind of interpolation in mathematics, namely the "interpolation of operators". The classical results about interpolation of operators are the Riesz-Thorin theorem and the Marcinkiewicz theorem. There also are many other subsequent results.