Let f(x, y) = xy - 4x on

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fxy.

A: Given:  Let fx, y=xy+x+x cos y To Find:  To determine fxy.

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

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Q: Let F (x) = (1 + + t4)1/4 dt · Then %3D F'(x) = %3D

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Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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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: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: Given:          F(x)=∫−2x(t2−2t)dt

Q: Let F (x) = (1 + t2)/4 dt - Then %3D F'(x) =

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Q: Let F(z, v)-v +y+3z+1-0

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Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). F(x) = 1 + t3 dt

A: To find F'x Fx=∫0xt21+t3dt

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: 19 If f(x) = t dt then %3D f'(x) =

A: Given that  f(x) = ∫x19t4 dt  Here we have to find f'(x) .

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

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Q: Let F (x) = %3D In tdt then F' (x) = et3

A: To find F'(t)

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: To find F'x using the second fundamental theorem of calculus: Fx=∫-1xt4+1dt Solution: The second…

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: Let F(x, y) = G , y 1 )- Calculate the work against F required to move an object from (1, 1) to (3,…

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Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: Let f(x, y) = − sin2 (2x − y) Evaluate fx and fy at (π / 4, π / 3)

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Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

Q: Let f(x, y, z) = -2xy − xz + 3yz + 1⁄x² + 3y² + z². - The set of critical points of f is

A: Given: fx,y,z=-2xy-xz+3yz+x22+52y2+z2 To find: The set of all critical points of f.

Q: Let F (x) = (1 + t2)/5 dt - Then F'(x) =

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Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

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Q: Let f(x, y) = (- (3x + y))'. Then %3D drðy af

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Q: If Tn,0(x) = ao +a¡x+ a2x² +.. he function f(x) centered at x = %3D -) True p) False

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

Q: Let f(x,y)=x°-4y where 0<x <1 and 0sysl. Find the minimam of value of f(x,y).

A: Answer

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: Let f(x,y) = xcosy – ye*y. fry at (1,0)is equal to: -1 -5

A: fx is partial derivative with respect to x fy is partial derivative with respect to y

Q: Let Find the f(x) = = d Le dt. م الموقع the inter Lo

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Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: It is given that,Fx=∫-2xt2-2tdt We have to use the Second Fundamental Theorem of Calculus to find…

Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

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Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Estimate the global maximum value for the function F on the interval [-2,1] if F(x)= || dt . t2 +1

A: The given function is: F(x)=∫-2x tt2+1 dt

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

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Q: show that the L operator is linear for y" – 4y" + 2y' + y = x2

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Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: Let f(x, y) = (x² +(3))°. Determine the directio %3D 4)

A: