4. Evaluate fe fds where f(r, y, z) , ) and 0

Q: If X(t) with X (0) = 0 and µ = 0 is a Wiener process, show that Y(t) = oX %3D is also a Wiener…

A:

Q: If y is implicitly defined as a function of e by –2 + + cos(y) = 3, determine de ysín(oy) + 2 -1…

A: We have to find dy/dx.

Q: Let C be the shortest path that connects a to ni and I = S, (coshz – 1)dz. Then %3D O I=-sinh n+…

A:

Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

A:

Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

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Q: 6. Let u (r, t) be the solution of the initial-boundary value problem ut = 9uzz 0 0, %3D uz (0, t)…

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Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

A: It is an important part of statistics. It is widely used.

Q: Let C be the shortest path that connects z to mi and /= . (sinhz + 1)dz. Then |=-1-cosh t+ n(1-1)…

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Q: 8 (6562) 243 를-), then xo = If the length of the curve y = 3 x7 from the point (0, 0) to the point…

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Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 2(3) Calculate the following commutators: (a) [d/dx, x·d/dx] (b) [sin(x), cos(x)] (c) [x^2, Ĥ] ,…

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Q: 3) The circulation of W = p coso ao + z sino az around closed path L shown in figure, is: a) v3 - 2…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the following semilinear first-order PDE ди ди +y ду = xe (i) Find the general solution to…

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Q: 1+ni Q1. Evaluate " e*dz along the path shown in figure below. n/2 1

A: We evaluate given integral along the path

Q: In each of the following problems, find the Wronskian W(y1,y2)(x) of the given list of functions and…

A: By using determinant and derivative of functions we solve the given problem.

Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

A: We have to find the value of  ∫Cxy dx + y2+1 dy. Given the path C is

Q: Let C be the shortest path that connects a to ni and I = S. (sinhz +1)dz. Then None of these O…

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Q: Let F(x, y, z) = (2x cos(y), e² – x² sin(y), ye²). (a) If possible, find all potential functions for…

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Q: 2) Use Green's Theorem to compute f F. df where F=(3x +4y) i + 2xyj and C is the triangular path…

A: Use green's theorem

Q: 2) Use Green's Theorem to compute f F df where F=(3x + 4y)i + 2xyj and C is the triangular path from…

A:

Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: (1. 1. 1) Evaluate the integral (5xy + 22°) dx + 5xf dy + (12z + 1) dz. (0.0.0) (Hint. Try the path…

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Q: Consider h(x,y, z) = cos (xy) + eY² + In (xz) at the point P ( 1,0, = 1 Deter-

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Q: Let C be the shortest path that connects a to ni and I = J. (coshz – 1)dz. Then I=-sinh T+ T(i-1)…

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Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

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Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: |-4 Let y =||-3 and u =||-4 7 Compute the distance d from y to the line through u and the origin. d…

A: Solve for the distance

Q: 1. Let P, X,Q denote distinct points of E. If X is between Pand Q, show that d(P,X) d(X,Q) 1-t, for…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let C be the shortest path that connects t to ni and I = J. (coshz + 1)dz. Then %3D O I=-1-cosh t+…

A: Since you are asking multiple questions. We are answering only the first questions. Let C be the…

Q: 11 ComputePydz - zy'dy, nhere Dis descnbed by z² + y²s1. -1/2

A: Given an integral : ∫∂D x2y dx - xy2 dy  where D is : x2+y2≤1 We need to compute the integral.

Q: Compute, [(1 – ye-")dx +e¯*dy where C is any path from (0, 1) to (1, 2).

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Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: and further we require that u(r, z) is bounded as z - +oo. Find an expression for the steady state…

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz – 1)dz. Then |=-sinh n+ n(1-i)…

A: The solution is given by using line integral method as follows

Q: 1. Find the optium path for f=xy³ from (2,1,2)

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Q: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: 1. Evaluate | (x- y)ds over the path C:r(t) = 4ti + 3tj for 0 <t<2.

A: Answer

Q: IF Y = u²-1 u²+1 Find dy np

A: Given,  y=u2-1u2+1

Q: 2/ Compute fc E.dr and Where F Gxry2=(3+ 12x²,3xy²2 is a line segment from Co,01 to (4,2) %D Fdr =

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Q: Given F(x, y) = (2xe'6(y), e'x²(eY + 0(y)) with o E C'(R) then O (A) F is conservative only if o(y)…

A: (A ) is true.

Q: Given F(x, y, z) = (tan y + cosh x Joi 2xy)i + (x sec² y - x² + 1)ĵ - 2zk, evaluate F. dR where C'…

A: Given that,  F→x,y,z=tany+coshx-2xyi^+xsec2y-x2+1j^-2zk^, Therefore, set fx=tany+coshx-2xy…