what is the difference between discrete variable and continuous variable? can anyone give examples?
828433
A discrete variable typically fits into a category and is a yes or no answer.  They are tabulated into single events, i.e. broken = yes or no?.\n\nA continuous variable is something measured on a continuum, and can have an infinite number of values.\n\nA good test for this is to ask if it can be divided in half.  For example, Can something be half broken?  If is doesn't make sense to be, it is discrete.
794869
Here's a good website that discuss implicit differentiation with some example problems.\n\nHope this helps
101134
A function always outputs a value. Suppose the function \nf(x) = 10x+20, what this means is that this function outputs different values for different input values of variable 'x'. For example:\nf(10) = 10X10+20 = 120\nf(20) = 10X20+20 = 220\ni.e. we substitute different values into x and get different outputs. \nThe important point is that every function outputs a value.\n\nComing to Equations. Equations define the relationship between one or more variables.\nSingle variable equation:\nx2 - 10x = 0\nMulti vairable equation:\n2x+3y = 10\nAn equation doesnt output a value. We can solve the equation and find out the values of the variables. The equation would be valid only for certain values of the variables.\n\nHope the difference is clear.
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Independent variables are just that, independent of other variables. Dependent variables rely on one or more independent variables.\n\nFor example, your salary is determined by the number of hours worked. The number of hours is independent of any other variable. However, salary is dependent on the number of hours.
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The equation is continuous at both points but is not differentiable at either of them.\n\nYou have f(x)= Ix^2+5x+6I=|(x+2)(x+3)|=|x+2| |x+3|\n\nNear x=-3 |x+2| is continuous and differentiable because x+2 is strictly negative. The problem is that near x=-3 |x+3| is not differentiable. You basically follow the argument that you gave in your problem statement. So you have something like this:\n\nf(x)=g(x)h(x)\n\nwhere g(x)=|x+2| and h(x)=|x+3|. Using exactly the argument that you provide h(x) and g(x) are continuous at x=-3. However, h(x) is not differentiable while g(x) is so the product is not differentiable.\n\nFor the case x=-2 you basically use the exact same reasoning for this new point. Again, you express f(x) as the product of g(x) and h(x) and then use the same argument that you provide in your problem statement.
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YES !!!\nA variable y is a function of x if a relation between x and y produces exactly one value of y for each value of x.\n\nThis is not a higher education question !
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Your 5-day mean, while it has a smaller interval, is less accurate.  Your 10-day mean, while it has a larger interval, is more accurate.  To better understand this without math, its best to understand that as your number of samples goes up, your data will "normalize", or approach a consistent distribution.  While it is impossible to say within what finite range, with 100% accuracy, your mean will fall, your interval will become more and more accurate as your number of samples increases.  So, as per predicting the results after tomorrow's data is entered, your 10-day mean is more accurate.  Understand also, though, that neither mean is a tool for predicting the results of tomorrow ALONE, rather they are tools of predicting the interval after tomorrow's data is ADDED to the data ALREADY COLLECTED.\n\nSteve
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basically, think of a function as a machine:\n\ntake this an an example: f(x) = 2x +3\nsee the x in brackets?\n\nif x = 1, then f(1) = 2(1) + 3 = 5\nif x = 2, then f(2) = 2(2) + 3 = 7\nif x = 3, then f(3) = 2(3) + 3 = 9\n\nsee whats happening? the answer DEPENDS on number inputted in the brackets.\n\nso therefore, the definition you quoted "a consistent, predictable, relationship between the independant and dependant variable" is true.
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Qualitative variable: variables which differ in "types" and can not be ordered (e.g. gender, species, method). \nQuantitative varaible: \n\nQuantitative variable :. variables that differ in amounts or scale and can be ordered (e.g. weight, temperature, time).\n\nDiscrete variable: A variable that assumes only values in a discrete set, such as the integers. (eg gender - can be only male or female, or number of things - can only be 1, 2, 3... not 2.3 things).\n\nContinuos variable: if between the values of the variable there can be other values (eg length - can be 2.3m or something, or age - can be 1 year 3 months 5 days)\n\nDichotomous - Variables that can only take 2 different values (eg. male or female)\n\nMultinomous - variables that can take more than 2 different values.
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Given: f,g: R → R continuous\nSo,|x - c| < &#92;del ==> |f(x) - f(c)| < &#92;epi.             (i)\nand\n|x - c| < &#92;del ==> |g(x) - g(c)| < &#92;epi.                (ii)\n\nNow,\nLet h(x)=max {f(x),g(x)}.\n\nTo Prove: h(x) is continuous.\n\nProof:\nTo show h(x) to be continuous it is enough to show that the following holds...\nfor |x - c| < &#92;del ==> |h(x) - h(c)| < &#92;epi.           (iii)\n\nObserve from (i) and (ii) that \nfor |x - c| < &#92;del ==> |max{f(x),g(x)} - max{f(c),g(c)}| < &#92;epi                                                   (iv)\n\nSince f(x) and g(x) is continuous in (x - &#92;del, x + &#92;del) interval. Max{} is bounded. And hence (iv) is true.\n\nSo by (iii) h(x) is continous.
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Discrete means individual and noncontinuous. There is "space" between consecutive elements. In discrete mathematics, you do a lot of counting. Some topics grouped under discrete mathematics include game theory and graph theory.
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1 is false. The function is continuous.\n2 is false; see above.\n3 is true.  Hence, 4 is false, and so is 5.\nYou are right about the non-differentiability at x=3.  A function cannot be called differentiable if its slope at x- does not approach its slope at x+ as the interval approaches zero.
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Discrete Signal :\nObtained by sampling the analog signal at disctrete instants of time. However the magnitude of the discrete signals is same as that of the analog signal at that point in time. (Discrete only in time)\n\nDigital Signal :\nWhen the magnitude of the discrete signal is quantized to the the nearest integer, we get a digital signal. (Which is both discrete in magnitude & time)\n\nExample:\nSay, after sampling the analog signal, we get discrete signal as below\nx[0] = 0\nx[1] = 0.9\nx[2] = 1.8\nx[3] = 2.6\nx[4] = 2.1\nx[5] = 1.8 ....\n\nWhen you want to digitize this signal, you pass it through the ADC & the output would be as below.\nx[0] = 0\nx[1] = 1\nx[2] = 2\nx[3] = 3\nx[4] = 2\nx[5] = 2...\n\nThe above output depends upon the resolution of the ADC .\nMore the resolution, less the quantization error.\n\nI hope i answered your question.
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An Input Variable is something which you put into an experiment - so say a certain amount of chemical you put in being changed.\n\nThe Output Variable is the results you get, which will obviously change.\n\nTom Walvin\nBiology/Chemistry Student
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Thats pretty basic.  The control in the experiment is the constant.  Something that has a predictable outcome.   The variable is the item that you are experimenting on.\nKind of like haveing a placebo in a drug test...
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--- An informal definition of a continuous function is a graph that can be drawn without picking up your pencil.\n--- This graph, however, is NOT differentiable at the point x = 0 because it is a cusp, i.e., the slope of the graph from the left is not equal to the slope of the graph from the right.\n--- If you take the derivative, you get -(2/3)x^(-1/3). If you substitute in x = 0, you get an undefined derivative. i.e., not differentiable at x = 0.
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y is a function of x and in a linear way, so one can say that y is a linear function of x,\non the other hand, y=x+5 is a linear equation in 2 variables x and y.\n\nthe difference between function and equation is whether you can write a variable as a function of the other or not: for example:\nx^2 + y^2 =1 is an equation in 2 variables, but it is not a function... or more precisely you cannot get a function from it, since you would need to use the square root (at some point).\n!