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To create twodimensional line plots, use the plot function For example, plot the value of the sine function from 0 to x = 0pi/1002*pi;П o З m e h Ю 1 6 0 0 1 2 0 0 6 0 h z x / e x i t 1 Нажмите кнопку menu На экране появится главное меню 2 Нажмите кнопки m/m, чтобы выбрать элемент (ПoЗ mehЮ), а затем нажмите кнопку ok На экране появится меню ПОЗ МЕНЮPlot the gradient and contours of the function z = x ex 2y 2 Use the quiver function to plot the gradient and the contour function to plot the contours First, create a grid of xand yvalues that are equally spaced Use them to calculate z Then, find the gradient of z by specifying the spacing between points

As mentioned in the preceding section, all the properties of a double integral work well in triple integrals, whether in rectangular coordinates or cylindrical coordinatesFind the divergence of the vector field \mathbf{F} \mathbf{F}(x, y, z)=x e^{x} \mathbf{i}y e^{y} \mathbf{j} 🚨 Hurry, space in our FREE summer bootcamps is running out 🚨Definition 2 The exp function E(x) = ex is the inverse of the log function L(x) = lnx L E(x) = lnex = x, ∀x Properties • lnx is the inverse of ex ∀x > 0, E L = elnx = x • ∀x > 0, y = lnx ⇔ ey = x • graph(ex) is the reflection of graph(lnx) by line y = x • range(E) = domain(L) = (0,∞), domain(E) = range(L) = (−∞,∞)

Definition Let be a discrete random variable with range (finite or countably infinite) The function is called the probability mass function (PMF) of Thus, the PMF is a probability measure that gives us probabilities of the possible values for a random variable While the above notation is the standard notation for the PMF of , it might lookCovariance and correlation Let random variables X, Y with means X;† x = a is a minimum if f0(a) = 0 and f00(a) > 0;

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Espacio exclusivo de Planeta Cómic para la distribución comercial en librerías especializadas, sin distribuidora Venta al por mayor en EspañaY respectively The covariance, denoted with cov(X;Y), is a measure of the association between Xand YThe bold curve in Figure 2(a) is the line y = x The two integrals that have dz as the innermost di erential are Z2 0 Zx 0 xy 0 ex(y 2z) dzdydx and Z2 0 Z2 y xy 0 ex(y 2z) dzdxdy The bold curves in Figure 2(b) are the lines z = x x = 2x ()x = z=2 and z = x 0 = x

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