3x+y-9 V3x+y-3 6. if 3x +y + 9; Let f(x,y) = %3D if (x,y) = (3,0). Then f is continuous at (3,0). f is not continuous at (3,0).

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

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Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

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Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: If f(x, y) = x3 + yt, what is the partial derivative of f with respect to x? A 3x2 B 4y3 3x²+ 4y3

A: Given fx,y=x3+y4

Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

Q: 1. Find the first and second partial derivatives (that is f, af, , , and ) of Əx' dy' dx², ay² »…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: (5) The partial derivatives of f = f(x, y) are f. = 6(x² – 1)(y + 1), - fy = 2.r(x? – 3). - Find all…

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

Q: 2x – 5y (1, y) # (10, 4) Find C so that the function f(x, y) = V2r – 5y +4 – 2 C (x, y) = (10, 4) is…

A: Given function is fx,y=2x−5y2x−5y+4−2, x,y≠10,4C                        , x,y=10,4 Given function…

Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

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Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: Q2: Find the Partial Derivatives of the functions with respect to each variable x and y and z: 1.…

A: 1. Given function is, f(x,y)=sin2(x-2y) Now, ∂f∂x=2sin(x-2y)×cos(x-2y)…

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: Find the partial derivative of fy for the function 3 f (1, y) = (3x² +y²)* 6 (3æ² + y°)? 32 (3x² +…

A: To find: The partial derivative fy of fx,y=3x2+y23. Given: The function is fx,y=3x2+y23. Concept…

Q: Find the partial derivativef,for the functionf(x,y) - &x+y. 1,(x.y)- 17 1,(x.y) = Sx+y Sx ,(1.y) =…

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Q: Q4) The critical points of the function f(x, y) = 8y³ – 12xy + x³ O (0,0) and (1,2) O (0,0) and…

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Q: -2? + 15z - 27 f(z) = 3z2 + 7z + 6 C, I= 3 What value of C would make f(x) continuous at z = 3?

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

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Q: * (0,0) is not continuous if (x, y) Q.3 ( 3+3+4) (a) Prove that the function f(x,y) = {2x+y (i if…

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Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(1, 1) =

A: The given function is;  f(x,y)=ln(x+y-1).

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

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Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

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Q: 114 f(x, y) = (xy²-1 y-1 tion f(x, y) at the point (1,1), where (x, y) = (1,1) (x, y) = (1,1)

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Q: Find the partial derivative. 2) Let z = f(x.y) = 8x2 - 12xy + 4y3. Find z ax A) 16x + 12y2 C) 16x -…

A: As per our guidelines we are suppose to solve only one question if the multiple questions are…

Q: Find fy(x,y) and fy(x,y). Then, find fy(- 3,1) and fy(1, – 4). f(x,y) = In |7 + 4x°y²|

A: Let f(x,y) be the given function .Then fx is the derivative of f with respect to x  , treating y as…

Q: 1 (x, y) = (1, –1) f(x, y) = x2 + Y (æ, y) + (1, –1) x + y is not continuous at (1, –1). [b]

A: Given :    f(x, y) = 1 ,(x, y) = (1, -1)x2+yx+y ,(x, y) ≠ (1, -1) To show :   f is not continuous at…

Q: x³y 3. Determine if f(x,y) is continuous at (0,0). %| x6 + y2 trial paths: X = y x = y? y = x³

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Q: dy + 2xy = f(x), y(0) = 6, where dx f(x) = lo, x, 0sx< 1 x 2 1 0 sx < 1 y = x 2 1 Use a graphing…

A: Linear differential equation of first order : The most general form of a linear differential…

Q: dy Find a continuous function function y on (-0,00) satisfying -6/7 = 9x dx and y(-1)= -4. dy -6/7…

A: Given query is to solve the differential equation.

Q: Find the partial derivative. f(x,y)=x^3+5x^2y-8xy^3. Find fy(x,y)

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Q: ди ди + 2х. -00 1, t- 1, a + 2x- dt dx и(х, 1) %3D f(x).

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Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

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Q: The function f(x,y)=xy(1−5x−4y)   has 4 critical points. List them and select the type of critical…

A: The given function can be written as follows.

Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: Find the linearization of f(x)=1−∫3x+124/(3+t)dt at x=2.   upper limit of integral = x+1 lower…

A: Linearization

Q: 2. Let f(x,y)= xe" and find a) fu. fy» fy

A: Please refer the attached image for complete solution.

Q: Find the partial derivative for the function f(x,y)=√x+y3 f(xx,y)= f(x,y) = √8x + y² 33x √8x+y³ (y)=…

A: The given function is;  f(x,y)=sqrt(8x+y3).

Q: 2. i) Give an example of a nonzero continuous function f on [0,1] such that f(x)dx = 0.

A: We have to give an example of a nonzero continuous function f  on [0,1] such that  ∫01f(x)dx = 0

Q: Find fzyx If f (x, y, z) = ln(x2 + z) + y2exz

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Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

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Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

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

Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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

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Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: 以く2 g(x) = X = 2 *一2 h continuous at MArDl (0,2]

A: The given function is: g(x)=x2+1, x&lt;25        ,x=21x-2,x&gt;2