14. Show that the function f: R²R given by if (x, y) 0, ²+y² f(x, y) 0 if (x, y) = (0,0), is continuously differentiable and has all its second order partial derivatives, but 8² f - (0,0) əxəy 8² f əyəx -(0,0)

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: 2. Prove B = { :n e N} U {0} is compact. %3D 3. Let F = {Fa : a € A} be a family of compact sets.…

A:

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

A:

Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down.…

A:

Q: 2. Determine the directional derivative of o(x, y, z) = re" + y² + xyz at the point (2, 0, 3) in the…

A:

Q: The equations zy? + 8xzcos(u) + ye" = 16 and r*yz+xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: Find all second partial derivatives of the function f(x, y) = xy + x° + y at the point xo = (2,4). =…

A: Consider the case of a function of two variables, f(x,y) since both of the first order partial…

Q: Give an example of ANY one nonlinear (i.e. powers of r, y can't just be 1) function z f(r, y) such…

A:

Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: Find all the first and second order partial derivatives of f(x, y) = −4 sin(2x + y) + 10 cos(x - y).…

A: Given:- fx,y=-4sin2x+y+10cosx-y

Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: of ) Find the first order partial derivative of and for the function f (x, y) = x/y -x²y+y² ây

A:

Q: A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x² – y? + 6y if they open a…

A:

Q: 1 Find the partial derivative with respect to y of the function (2 x – 3) (3 y + 1)i el-5 z+5). -5…

A: To find the partial derivative of the given function with respect to y (2x-3)1/4(3y+1)1/4e(-5z+5)

Q: Let ƒ (x, y) = x³ − x² − 8x + 2xy − - - 12y². (a) Compute all first order and second order partial…

A:

Q: I got this answer wrong

A:

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

A:

Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

A:

Q: Find the first partial derivatives of f(x, y, z) af A. (5,5,-2) = B. of (5,5,-2) მყ = C. (5,5,-2) =…

A:

Q: 10.J Compute the matrix of partial derivatives of: f(x,y) = (x+y, x-y, xy) d.) f(x, y, z) =…

A:

Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

A:

Q: dz (е) dz

A:

Q: Solve the partial differentiabion equation +6.0 = 2-y Ox Show that the gereral aoludion 2.

A: Given. the partial differential equation                            ∂2z∂x2+5∂2z∂x∂y+6∂2z∂y2=2x-y…

Q: 5. a) Find the first order derivative of the following function. y x° In x

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Find the value of at the point (1, 3, 1) if the equation 6xz + ylnx – 5x² – 1 = 0 defines x as a…

A: Given equation is, where x is a function of two independent variables y and z and the partial…

Q: Let – 4x – 2y – 5z* – 4xyz + 619 = 0. az Use partial derivatives to calculate dz at the point (6, 5,…

A: let -4x3-2y3-5z3-4xyz+619=0 to calculate  ∂z∂x and ∂z∂y at the point 6,5,-3

Q: 다음 함수 /의 2계 편도함수를 모두 구하여라 (1) fx, y, 2) sin (xy) cos (vz)

A: As per Our guidelines we can solve maximum one question u can repost other's in next question

Q: 6. Find the gradient of f(x,y) = ,x' - u°. grad f i +

A: We will find the first order partial derivatives with respect to x & y and use the definition of…