3. Which of the following represent linear function? a) 3x = 20-4y b) y-4 =0 c) x' +3y = -10 d) y = Jx+7

Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Show that: H(X,Y) = %3D H(XY) + H(Y)

A: We have to show that H(X,Y)=H(X/Y)+H(Y)

Q: (c(2z+y), %3D ue of c in the joi F of W.

A:

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

A:

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

A:

Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

A:

Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

A:

Q: Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate…

A: Given,f(x,y) = x2y2+1To estimate,f(4.02,0.93) using the LinearApproximation at an appropriate point…

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

A:

Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

A:

Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

A:

Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

A:

Q: If Wly, , y2. Yal = 0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

A: Given that if  W[y1,y2,y3]=0, then {y1, y2,y3} must linearly dependent, where y1,y2,y3 are…

Q: Calculate f. x²dx + xydy where C consists of the straight line segment from (0,0) to (1,1), followed…

A: Proceed as shown below

Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

A:

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

A:

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

A:

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Suppose that Vf(x, y, z) = 2xyze*i+ ze**j+ ye*´k. If f(0, 0, 0) = 5, find f(1, 1, 8). Hint: As a…

A:

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

A:

Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

A:

Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

A:

Q: (a) Assume that traffic flows at a rate of 240 vehicles per hour on the stretch of road between…

A: The number of vehicles coming and leaving the signal is same in all the signals. That is, Total…

Q: B. Use the definition of directional derivative to solve Duf(x0, Yo, zo) at point P(xo, Yo%o) where…

A:

Q: 9. Demonstrate that the functions Y1 = x2, y2 = sin(x), y3 = xe are linearly independent on R.

A: Recall: If y1,y2 and y3 are the given function and         Wy1,y2,y3x = y1y2y3y1'y2'y3'y1''y2''y3''…

Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

A:

Q: Find the linear approximation to f(x, y, z) = at the point (3, -2, -2): f(x, y, z) Z

A: To find the linear approximation of the below function at the point 3,−2,−2. fx,y,z=xyz

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Obtain the DE of the family of lines passing through (2,0). Select one: о 2ydar — (z — 1)dy o (x –…

A: We find the differential equation of the family lines passing through (2 , 0)

Q: Determine the linearization of y = 4 – 2x at (1, 2). Then use it to approximate the value of y when…

A: It is given that, y=4-2x2  at 1,2 we have to determine the linearization of function. Then use it to…

Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: Find the image of the line z =3 +iy under f(z) = e

A:

Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

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

A:

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

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

Q: 2. Suppose that a function f: R3 → R³ defined by: f (х, у, 2) 3 (2х + Зу — z, sin(тхy?z-1),…

A:

Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

A: