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If Eis an extension of F and α∈ Eis a root of a polynomial f ∈ FX, it is often ofinteresttoexaminethefield F ( α )generatedby F and α ,inotherwordsthesmallest subfield of E containing F and α (more precisely, containing all elements of F along(Leting g(x) = xn yields moments for example) Finally, the variance of X is denoted by Var(X), defined by E{X − E(X)2}, and can be computed via Var(X) = E(X2)−E2(X), (2) the second moment minus the square of the first moment We usually denote the variance by σ2 = Var(X) and when necessary (to avoid confusion) include X as a subscriptThe different sine integral definitions are ⁡ = ∫ ⁡ ⁡ = − ∫ ∞ ⁡ Note that the integrand sin x ⁄ x is the sinc function, and also the zeroth spherical Bessel functionSince sinc is an even entire function (holomorphic over the entire complex plane), Si is entire, odd, and the integral in its definition can be taken along any path connecting the endpoints

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E^x get x

E^x get x-Probability distribution definition and tables In probability and statistics distribution is a characteristic of a random variable, describes the probability of the random variable in each value Each distribution has a certain probability density function and probability distribution functionDomain of Composite Function We must get both Domains right (the composed function and the first function used) When doing, for example, (g º f)(x) = g(f(x)) Make sure we get the Domain for f(x) right,;

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Conditioning on the discrete level Example A fair coin is tossed 10 times;More generally, Eg(X)h(Y) = Eg(X)Eh(Y) holds for any function g and h That is, the independence of two random variables implies that both the covariance and correlation are zero But, the converse is not true Interestingly, it turns out that this result helps us proveV = e x , v = e x (Note that the antiderivative of v is no more complicated than v was — another indication that we've chosen correctly) On the other hand, if we used u = ex, then u = ex would not be any simpler Performing the integration by parts we get x n e x dx = x n e x x n −1 e x dx − uv uv u v If G n(x) = x n e x dx then we

∫x e x dx Solution According to the above property ∫ x e x dx = ∫ x dx ∫ e x dx ò x dx is given by 13 and ∫ e x dx by 41 in table of integral formulas, hence ∫ x e x dx = x 2 / 2 e x c 4 Integral of Difference of Functions ∫f(x) g(x) dx = ∫f(x) dx ∫g(x) dx Example Evaluate the integral ∫2 1# d/dx \ int_1^x e^(t^2) \ dt = e^(x^2) # Explanation If asked to find the derivative of an integral then you should not evaluate the integral but instead use the fundamental theorem of CalculusSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more

Then also make sure that g(x) gets the correct DomainThe random variable X is the number of heads in these 10 tosses, and Y — the number of heads in the first 3 tosses In spite of the fact that Y emerges before X it may happen that someone knows X but not Y Conditional probabilitySuppose that X is a random variable with EX^2 < ∞ Show that g(t) = E(X − t)^2 is minimized at t = EX and that no other value for t attains the same minimum value (ie t = EX is a unique minimizer) Think about what this result implies

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Discutir a quantidade de soluções reais de uma equação `g(x) = f(x)` pode ser facilitada pela exibição no mesmo plano cartesiano dos gráficos de `g(x)` e `f(x)` Dispensando o uso de calculadoras e/ou programas CAM (computer aided mathematics) um bom esboço dos gráficos de f e g vai ajudar a análise da equação que as envolveNow from here, as x grows larger (eg, x = 10, 100, 1000, etc), the values of the height y = 1 x eg‚ 1 10 = 01‚ 1 100 = 001‚ 1 1000 = 0001‚ etc become smaller, although they never actually reach 0 Therefore, as we continue to move to the right, the graph approaches the Xaxis as a horizontal asymptote, without ever actuallyCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history

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Experts are waiting 24/7 to provide stepbystep solutions in as fast as 30 minutes!*Go X provides the most advanced electrical vehicles for anyone to rent Experience your city like you have never before by riding our 2wheel and 3wheel scooters Go X Scooters are designed to be safe, reliable and convenient They are capable of going up to 25 mph and last 30 miles on a single charge They are weatherproof, durable and most importantly safeMath(0,1)/math is on mathf(x)\implies (1,0)/math is on mathg(x)/math math\begin{align}\text{Since }g(x)&=f^{1}(x)\\f\circ g&=x\\f(g(x))&=x\\f'(g(x

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Normally this is the result limx→∞ e x x 2 = ∞∞ Both head to infinity Which is indeterminate But let's differentiate both top and bottom (note that the derivative of e x is e x) limx→∞ e x x 2 = limx→∞ e x 2x Hmmm, still not solved, both tending towards infinityThen also make sure that g(x) gets the correct DomainCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel knowledge and

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For any function g, the mean or expected value of g(X) is defined by E(g(X)) = sum g(x k) p(x k) Ex Roll a fair die Let X = number of dots on the side that comes up Calculate E(X2) E(X2) 2= 2sum_{i=1}^{6} i p(i) = 1 p(1) 2 2 p(2) 32 p(3) 42 p(4) 5 p(5) 62 p(6) = 1/6*() = 91/6 E(X) is the expected value or 1st momentWe're going to replace the x with g of x So, f of g of x is going to be equal to the square root of Well instead of an x, we would write a g of x g of x, g of x squared g of x squared, minus one Now what is g of x equal to?Domain of Composite Function We must get both Domains right (the composed function and the first function used) When doing, for example, (g º f)(x) = g(f(x)) Make sure we get the Domain for f(x) right,;

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