Find fy and fy, and evaluate each at the given point. f(x, y) = arctan(), (6, -6) fx(x, y) = f,(x, y) =| f(6, -6) = f,(6, –6) =|

Q: 19. f(x, y) = x + y+y+ 1, constrained to the triangle with vertices (0, 1), (-1,–1) and (1, +1). %3D

A: As per bartleby guidelines i can answer only one question, kinldy upload rest questions separately.…

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

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

Q: D. On what point/domain will the f(x, y) = Vx ey will be continuous? Explain your answer!

A: Solved below

Q: Example H·W: for f(x,y) = cos(xy) - x3 + y compute fxyy, fxxyy

A:

Q: Find f, and f,, and evaluate each at the given point. f(x, y) = arctan A, (2, -2) | fx(x, y) = %3D…

A:

Q: Example: » - ( ) F(r,y) = | x² + y² ' x² + y², on the curve C : R(t) = (cos t, sin t), t e [0, 27].…

A: Given : vector field F→x, y=-yx2+y2, xx2+y2 on the curve C : R→t=cos t, sin t , t∈0, 2π

Q: Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

A: To Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A:

Q: For x = x(y + 3), y = y(x - 1), find the trace of the Jacobian at the fixed point x = 0, y* = 0.

A: Given system is x˙ =xy+3y˙ =yx-1 Fixed point :  x* =0, y*=0   Take   x˙ =fx, y,    y˙ =gx, y   then…

Q: Evaluate fx and fy at the given point. f(x, y) = e¹³y sin(x), (π, 0) fx(π, 0) = (No Response) fy(π,…

A:

Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: Determine fzz, fyy, and fz for f(x,y,z) = x²y³z – y sin(xz) + e».

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

Q: ad curl F if F(x, y, z) = xz7i+ 5y¹¹x²j + 6z²yk. d with CamScanner

A:

Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: Show that each function satisfies a Laplace equation. 1.ƒ(x, y, z) = 2z3 - 3(x2 + y2 )z 2. ƒ(x, y) =…

A: For a function f(x,y,z) to  satisfy a Laplace equation, it has to fulfill the following criteria.…

Q: 2. Let F(t) = (e' cos t) î+ (e' sin t)j+ek. a. Find symmetric equations of the line tangent to the…

A: Given:  F→t = et costi^ +et sint j^ +et k^  To Find:  Symmetric equations of the line tangent to the…

Q: If f'(x) = /cosec*x-1 then what is the arclength of the curve y= f (x) on со ? 3 A) 1 В) 3 C) 2 D)…

A:

Q: Find the Laplace of f(t) = (e-3t - e5t )2

A: To Find L(e-3t-e5t)2: Expand (e-3t - e5t )2: (e-3t-e5t)2=e-3t2-2(e-3t·e5t)+e5t2…

Q: Consider the sinusoidal function y = f(x) shown below. 8 6. 2- 10 15 20 25 30 35 -2- -4-

A:

Q: Fnd the orthogonal trajectorie of the family of curve r = c sin0

A: In order to find the orthogonal trajectories of the given curve, we need to differentiate it with…

Q: 04|| Find ôw/ôr and ôw/ôs as function of r and s, if: w = 2x + 3y² + 4z, X =r + s, y= cos (r - s), z…

A: Given   ω=2x+3y2+4z   x=r+s   y=cos r-s   z=erNow,      ∂ω∂r=∂ω∂x.∂x∂r+∂ω∂y.∂y∂r+∂ω∂z.∂z∂r→       1…

Q: Find f, and f, and evaluate each at the given point. y' f(x, y) ), (8, -8) = arctan fx(x, y) = f,(x,…

A:

Q: A. Find fxx, fyy,fyx, and fxy for the functions: 2. f(x, y) = In(xy) + tan(xy)

A:

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

A:

Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: fy = e*, y = 1 - e-x, and x = 0 ab- %3D

A: Given: - The curves of, y=e-x, y=1-e-x and x=0 about y=4.5 To find: - The volume of a solid is…

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: w=x2+y2+z2,  x=cost,  y=sint,  z=et a).…

Q: If a curve f(x) has dx dy = (y – 1)2(2+ x) and passes through the point (-1,2), then what is the…

A:

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

A:

Q: 2- Show that the function U(x,y)= 3x²y-y² + y is Harmonic and then find it's Harmonic conjugate V(x,…

A:

Q: Show that each function satisfies a Laplace equation. ƒ(x, y, z) = x2 + y2 - 2z2

A: Again differentiating with respect to x, we get Now partially differentiating given function with…

Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: Find fxx, fxy, fyx, and fyy if f(x, y) = sin²(x – 3y) %3D

A: f(x,y) = sin2(x - 3y) fx = 2sin(x - 3y)cos(x - 3y) fy = 2.(-3).sin(x - 3y)cos(x - 3y) = -6sin(x -…

Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

A:

Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

A:

Q: The values of fx , f y and f, at (1,1,1) for the function f (x,y,z) = x² + xyz +z are fy= Choose. +…

A:

Q: Find the point on the curve z = 5 sin(t), y = cos(t), - sts. closest to the point (2,0) . (Hint:…

A:

Q: Find f, and f, and evaluate each at the given point. y' f(x, у) ). (8, -8) = arctan fx(x, y) = f,(x,…

A:

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

A: Please refer the attached image for complete solution.

Q: Find fa, fy, and fz. f (x, y, z) = z In (x'y cos(22)) 5.4 fy = fz =

A: topic - partial differentiation

Q: Find the equilibria of the difference equation xt+1 = stable or unstable. If xo = 1/2 what is lim x?…

A:

Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

A: Given F→x,y,z=y2i^+2xy+e3zj^+3ye3zk^ and the curve is C given by r^t=cost,t,sint,  0≤t≤π2. Find…

Q: Consider F and C below. F(x, y) = x² i + y² j C is the arc of the parabola y = 3x2 from (-2, 12) to…

A: Consider Fx,y=x2i+y2j. a. We have to find a function f such that F=∇f. Step 1: We have…

Q: Find the equation of the tangent plane to z = e + x + x² + 4 at the point (3, 0, 17).

A:

Q: Find the function f(x,y,z) with a magnitude y.

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…