(a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

A:

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Let z = f(x, y) = 5x – x³ + 2xy – y². - Find and classify all the critical point(s) of this…

A: Differentiate the function fx,y=5x-x3+2xy-y2 partially with respect to x and y, to obtain fx and fy.…

Q: Find and classify the critical points of f(x, y) = 6xy – 4x³ – 3y?

A: According to our guidelines, we can answer only one question or three subparts of a question. other…

Q: Find the first partial derivatives of the function. f(x, у, 2) %3D хz — 7x8у^24 fx(x, Y, z) : %3D…

A:

Q: The partial derivative of the function f(x, y) = 4x² – 3xy + 5y-e³+8y with respect to x is: Select…

A: To find out the partial derivative of the equation.

Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

A:

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

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

A:

Q: 2. Find frxz for f(x, y,z)= z² e³xy

A:

Q: Let f(x, y) = x + y3 - 9xy+ 27 , then (0,0) is saddle point. True False

A:

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 25 L(x) =

A: The solution of the problem is given in the next step.

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

A:

Q: Find the linearization L(x) of f(x) at x = a. f(x) = Vx +15, a =7 %3D L(x) =

A: Givne that fx=x2+15, a=7To find L(x)

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: Find the Maximum and Minimum values of f(x, y,z) x +3y subject to the constrains x'+4y +z-36.

A: According to question,Given function,fx, y, z = x2 + 3y2,           ....1subject to the…

Q: DE 1. xy(5) y(4) + x²y"" = 2yy' TYPE ORDER DEGREE LINEARITY

A:

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

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

A:

Q: Y : k=0 y' + (2x + 1)y = 0, rrence relation. For k > 0,

A:

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Find the local minimum value of f(x, y) = 4+ x³ + y³ – 5xy.

A: Explanation of the answer is as follows

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

A:

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) 3x? – 7x…

A:

Q: Find and classify the critical points of the function f(x, y) = x²y+ 4xy – 2y².

A:

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

A:

Q: Find the local minimum value of f(z, y) = 4 + x² + y7 – 7xy.

A: Explanation of the answer is as follows

Q: Find the local minimum value of f(x, y) = 4 + x11 + yll – 11xy.

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Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

A:

Q: b. Find the partial derivatives fx ,fy of the f (x,y) = x². e²y+3x

A:

Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

A:

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: Find and classify the critical points of the function f(x,y) = x²y+ 4xy – 2y²

A: The given function is f(x,y) =x2y+4xy-2y2.

Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: Evaluate the indicated partial derivatives. f(x, y) = 3x°ye"y (& 6) af (a 3)

A: f(x,y)=3x6yexy

Q: Find the absolute maximum and minimum values of f(x, y)= 3+xy-x-2y on the closed triangular region…

A:

Q: If f (x, y) = Vr3 + y3 In (x² + y³)esin(zy+y') + x°y+ 10 , then f. (1,0) O 4

A: Properties of derivative  ddxex=ex ddxxn=nxn-1 ddxsinx=cosx ddx(lnx)=1x

Q: Find the linearization L(x) of y=e10xln(x) at a=1

A: y=e10xln(x)  The linearization L(x) of a function f(x) at x = a is, Now  Now differentiating given…

Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

A:

Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: Find the relative maximum and minimum values. f(x,y) = x° +y° - 3xy

A:

Q: Find the relative minimum value for the function: f(x,y) = e(5x2+8y2+4).  those 2's are "squares"

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Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

A:

Q: The function f(x, y) = 3x2 – 2xy + y2 – 8y has a saddle point at (0, 0). | Select one: True False

A: to find:- whether the given function has saddle point at (0,0) or not.

Q: Find the linearization L(x) of the function at a. f(x) = e5x, a = 0 %3D L(x) 1 + 5x

A: f(x)=e5x point a=0