Q2: Expand f(x, y) = [sin (x y*)] about E. 1). Q3: Given T(u) = sin (u), where u = x2 + y2, find T,-Ty-

Q: 2. Consider the PDE u; - t ux+tu=0 for - o <x< ∞ and 0 <t< ∞ with u (0, x) = sine x. Determine u (t,…

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Q: expand e cos y near (17) 1, by Taylor's Serios method

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Q: 4. (a) (b) Approximate the integral f x² cos xdx with n = 6 using the composite trapezoid rule;…

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Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: 5.) Suppose z = f (x, y) , where x=x(t,r) and y= y(t,r). Assuming all the functions involved have…

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Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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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: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

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Q: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

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Q: 4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z)…

A: Note:  Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: Use an integrating factor to solve the IVP y'+ytan x = cos x, with IC (x, , Yo) = (0,7), %3D and…

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Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

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Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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Q: Suppose that w = x² + y² – z² | And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: Simplify w by substituting values of x , y and z and then solve the partial derivative.

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: Əz 1 Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), yusin v, use chain rule to find : 201 ди and az

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Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 3n/2 %3D

A: We have to find the linearization L(x) of the given function.

Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 8) Evaluate the integral: f[(2 t² −5)i +cos j+(2+4)3 k]dt

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Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…

A: Given: The joint p.d.f of Y1 and Y2 is defined by:

Q: Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du as…

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Q: 4] I Let w = 5 cos(xy) – sin(xz); x = 1/t, y = t, z = dw using an appropriate form of the chain…

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Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

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Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…

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Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: Q1) Suppose w =÷+ ?, x = cos² t, y = sin² t, z = ; Evaluate dw at t = 3, by using the Chain Rule dt

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Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x