given F:= exp(-y), where 0 < x < y What is Probability that ( x_bar^2+y_bar^2 < 5)
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Maximum divergence Within the cube {(x, y, z): | x | ≤ 1, | y | ≤ 1, | z | ≤ 1}, where does div F have the greatest magnitude when F = ⟨x2 - y2, xy2 z, 2xz⟩?Use integration by parts to evaluate the definite integral:∫3se^-4s ds with an upper limit of -0.9 and lower limit of -1.7
- Find the area of a triangle bounded by lines y=2x and x=1 by a.) single integration b.) double integrationDifferentiate f(z)=cosz if z=x-iy, giving the appropriate region on which, the function is analytical. Hint: Use the different of two angles formulaLet f be the function given by f(x)=sin(2x)cos(1+x). What is the average value of fon the closed interval 1≤x≤3 ?
