What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

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Q: Let f(x, y,z) = x² sin y + y e², where x =t + 3,y = net-1 and z = In 2t. dL at t = 1 is: 1-2n O -12n…

A: Given, fx,y,z=x2siny+yez, where x=t+3,y=πet-1 and z=ln 2t.   The objective is to determine dfdt at…

Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: Let f(x, y, z) = x² sin y + y e², where x = t + 3,y = net-1 and z In 2t. %3D df at t 1 is: dt %3D…

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Q: Evaluate fSS 6e(²+y²+z²)/² dV over B where B= {(x, y, 2) : x² + y² + z² < 1}. Take T = 3.

A: Since we have    x2 + y2 + z2  expression in the integral and region B is the sphere of radius 1…

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: Assume x and y are functions of t. Evaluate dt for 2xy - 2x + 4y3 = - 56, with the conditions = -…

A: Given      2xy-2x+4y3=-56 →           1      dxdt=-16, x=4, y=-2

Q: Suppose that f(x, y) : at which {(x, y) | 0 < x < 4, – x < ys va}. 1+ x D

A: Consider a given function:  The objective is to evaluate the following double integral of fx, y…

Q: integral f t^3 In t dt

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Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: Find the following for z = f(x, y) = x? +5x2y3-y. az %3D ax

A: FOLLOW NEXT STEP

Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

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Q: Find the artho gon al traje eteries to c°y" - 4y + x*

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Q: Let y(t) satisfies dy dt 3ty-t-t 1+t2 for t2 0, and y(t = 0) = 1. Show that y(t) S 1+t for t2 0.

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Q: 2. Let f(2) = 2°e* z + 0. What type of singularity does f(z) have at z 0? (Justify.) What is the…

A: the point z=0  essential singularity.

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: FIND THE LINEARIZATION OF f(x) = 2+ [,* dt at z= 1. %3D 1+ Lütfen birini seçin: a. L(x) = 2x – 4 b.…

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

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: 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: Let y(t) satisfies dy 3ty-t-t for t20, dt 1+t2 and y(t 0) 1. Show that y(t) S1+t² for t2 0.

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Q: 2. Let F(x) = re* %3D VE dt, find F'(x). t2+sint

A: Solution is given below:

Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: find (In t)² dt dr ds (rst-space) 18. se In r T/4 cln sec v 21 19. e* dx dt dv (tux-space) -00 4-q²…

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Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: E. Find the orthogonal trajectories to the curve y = ax²- acx (s held fixed. %3D where a

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

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Q: Find dy/dt at t=9 given that y= (u+2)/(u-1), u= (3s-7)2 and s= √t

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Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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Q: 2 Find the orthogonal trajectories of r=asin? 0 where a be the arbitrary constant.

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Q: Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3,…

A: Given that 4xey=12-ln729+6 lnx and the conditions are dxdt=6 , x=3, y=0  find dydt

Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: Find the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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Q: Consider the function: u = 2 ln /x² + y² Show that uzz + Uyy = 0. %3D

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