Q: Let f(x, y, z) = In(x² + 2) + y²e== – cos(2yz). Find fzyz- %3D
A: Given that: f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)
Q: ds-(s + et)dt=0 (find DE,prove if exact or not)
A: dsdt=s+et It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…
Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…
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Q: Solve using Laplace Transforms y"+4y = t-2 sin t; y(0)=-1, y'(0)= 2,
A: given differential equation isy"+4y=t-2sinty(0)=-1y'(0)=2applying laplace transformLy"+4y=Lt-2 sin…
Q: Use the total differential dz to approximate the change in z= 6-x² – y² as (x, y)moves from the…
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Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…
A: Let f(x,y)= 2xy , x=t/ln2 and y= lns Here we have to find the equation of the tangent plane to…
Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt
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Q: Solve using Laplace Transforms y' + y = tsin(t); y(0)=0 %3D
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Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.
A: We can solve this as follows:
Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…
A: Use formula of linear approximation
Q: Let h(y) = In(y In y). Find h' (y). Show your work.
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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…
A: See the details solution in below
Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey
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Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?
A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2
Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,
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Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +
A: Answer:- Given that, X and Y have jointly Gaussian distribution.
Q: (a) 3y' In (u) dy
A: We will use the ILATE rule in this example to solve the integral and for solving we use the formula…
Q: Use the differential dz to approximate the change in z = √4 − x2 − y2 as (x, y) moves from the point…
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Q: Show that f(x, y) = ln(x2 + y2) solves Laplace's equation, ∂2z ∂x2 + ∂2z ∂y2 =…
A: Given Laplace’s equation is
Q: integral f t^3 In t dt
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Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False
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Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates
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Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.
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Q: Let y = V5- z. Find the differential dy whenz= 2 and dr = 0.1 %3D Find the differential dy whenz= 2…
A: y=5-x
Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -
A: Given that f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx
Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = ex cos y at a. (0, 0), b. (0,…
A: Consider the following function: fx,y=excosy Differentiate fx,y with respect to x taking y as…
Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…
A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…
Q: Find g: R R, continuous in [0. ) and position in (0, ) satisfying g1) %3D )dt
A: Here we have, g:R→R, continuous in [0,∞) and position in (0,∞) Also given g(1)=1 and…
Q: Find up +Uy given that u (x,Y)s. (x,x)s
A: Given that ux, y=tanx3+mx2y2+my4m-x2-y2 To find ux+uy we follow the following steps calculate…
Q: Find aw in terms u and v if du w= In(x2+y2 +z²), x = ue" sin u, y = ue' cos u, z = ue"; (u, v) =…
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Q: Find the linearization L(x,y) of the function f(x,y) = e* cos (9y) at the points (0,0) and ...
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Q: Show that if the function f(x, y) = ecos-e-cosx, satisfies Laplace Equation.
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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.
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Q: dy sin(x + y) dx
A: Given , dydx=sin(x+y) Substituting u=x + y dudx=1+dydx Substituting dydx=sin(x+y) in dudx=1+dydx…
Q: Show that the function f(x, y) = In /x² + y² satisfies the Laplace equation. %3D
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Q: Verify whether the function f(z) = e^x (cos y + isin y) satisfies Cauchy- Riemann equations or not.
A: We know that cauchy-Riemann equations ux = vy and uy = -vx Here u = excosy and v = exsiny
Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)
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Q: Let y = 4ĩ. Find the change in y, Ay when x = 4 and Ax = 0.3 Find the differential dy when x = 4 and…
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Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1
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Q: b/ Show that the function satisfy Laplace equation f(x,y) = In /9xy+ 3y² %3D
A: Since you have asked multiple questions in a single request so we will be answering only first…
Q: Determine the linearization of f(x, y) = arctan(x² + y²) at
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Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…
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Q: find du/dt for u=4ysin(x)+xze^xy^2 and x=3s+t, y=ln(s+t), z=cos(st)
A: The objective is to find dudt, where u=4ysin(x)+xzexy2, x=3s+t, y=ln(s+t), and z=cos(st)
Q: how that the function satisfy Laplace equation f(x,y) = In /9xy+3y²
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Q: y sin x is an i E+ iy is a comp со
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Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣
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Q: Evaluate [xy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4). [Verify using Mathematica]
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- A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.a) Find the marginal pmfs of X and Y b) Find the conditional pmf of X given Y = 1A CI is desired for the true average stray-load loss ? (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with ? = 2.2. (Round your answers to two decimal places.) (a) Compute a 95% CI for ? when n = 25 and x = 53.7. , watts(b) Compute a 95% CI for ? when n = 100 and x = 53.7. , watts(c) Compute a 99% CI for ? when n = 100 and x = 53.7. , watts(d) Compute an 82% CI for ? when n = 100 and x = 53.7. , watts(e) How large must n be if the width of the 99% interval for ? is to be 1.0? (Round your answer up to the nearest whole number.)n = You may need to use the appropriate table in the Appendix of Tables to answer this question.
- Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)J 1 Given the above distribution: 1.Assuming that α is known, show that f (y;α, µ) is a member of the exponential family. 2. Identify the canonical linkLet X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?
- Consider a random sample X1, … , Xn from the pdff (x; u) = .5(1 + (THETA)x) -1 <= x <= 1where -1 <= theta <= 1 (this distribution arises in particlephysics). Show that theta = 3X is an unbiased estimator oftheta. [Hint: First determine mu = E(X) = E(X).]For a non-homogeneous Poisson process, the intensity function is given by λ(t) = 5 if t is in (1, 2] or (3, 4]; λ(t) = 3 if t is in (0, 1] or (2, 3]. Find the probability that the number number of observed occurrences in the time period (1.5; 4] is more than 2. Round answer to 4 decimals.f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.
- 1. Let ?(?) = 3 cos(?) + ? −? + 4. a. [4 pts] Compute the average value of ?(?) on [0,1]. b. [4 pts] Compute the average value of ?(?) on [0,10]. c. [6 pts] Compute the average value of ?(?) on [0, ?], for a general positive constant b. d. [6 pts] Take the limit of your expression from part c as ? → ∞. What does that say about the long-term behavior of ?(?)?E(Yn)? Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0 and limnYn =0a.s.1. Let X have a gamma distribution with α > 1. Show thatE [1/X] = 1/[θ*(α −1)]