3. Find A'( 4. Find Z'(L (x, y) (x-2. y+ 3) (x, y) (x+2,y-3) 21 YY -1/01 -4

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

A:

Q: For numbers 1-2, consider a plane bounded by the curves y=9-x² and y=x+3. 1. What is the desired…

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Q: Find the first partial derivatives with respect to x, y, and z and evaluate each at the given point.…

A:

Q: 2. If T = u? + v²,u = x+ y+z,v= ryz. Using the chain rule to find and when r = 1, y = 2, z = 3. Draw…

A: Given that: T=u2+v2u=x+y+zv=xyzx=1, y=2, z=3

Q: (2) Evaluate S. 2 - xy ds where C is the upper half of the circle centered at the origin of radius 1…

A: Evaluate.

Q: Find all second-order partial derivatives for the following. 4.6 R(x,y) = 5x - 2x y° + 6x°y7 %3D 3.7…

A: Partial differentiation means , when we differentiates a function of more than two variables then we…

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A:

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A: y=ax3+bx2+cx+d-1Critical points 1,0-2,27We know that at critical point dydx=0 or does not exist…

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

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Q: The inflection point for y in the interval [0,15] is located at (give both coordinates!):

A:

Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

A:

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

A: Given curve is y=ax3+bx2+cx+d        (1) and critical points are (1, 0) and (-2, 27) We have to find…

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

A:

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

A:

Q: 3.4 Find the first partial derivatives of f(x, y) = 7x°y* + 9x y° +3. df = 21x y" + 18xy dx of %3D…

A: solution

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: Find the different partial derivatives of the following function and remember to show your work for…

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Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: 3) Evaluate elz+y)/(z-y) dA where Ris the quadrilateral with vertices (0,1), (0,-2), (1,0), and…

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Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³= 4x²y³ Determine dy/dx…

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Q: 7. Show that the horizontal lines y = 1 and y = -1 are asymptotes of y = tanh a and y coth r. %3D…

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Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the distance from the point (3, 4, -1) to the plane lr 3y +2z = 5.

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Q: 6 of 9 > Find an equation of the tangent plane to the surface at the given point. 2x² + 2y² + 4z² =…

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Q: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: The base of a three-dimensional figure is bound by the line x = y² and the y-axis on the interval…

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Q: 94: For the system presented by the function x +y+ 2 4xy. Calculate all the possible points at which…

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Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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

Q: The surface of a hill above the xy-plane is described implicitly by 3x² + y² + (z + 1)² = 2, z ≥ 0.…

A:

Q: Find all second-order partial derivatives for the following. 5 6,5 4.7 R(x,y) = 6x° – 8x°y$ + 3x*y7…

A: We have to find derivative

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

A:

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³ = 4x²y³ Determine dy/dx…

A: See this solution in below

Q: 1. Consider the function f(x, y) = {√x² + y² if x # (0,0) 0 if x = (0,0) Evaluate f(x, y) over the…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: 1. Find the orthogonal trajectories of the family of curves y³ = 3(x – c). Draw a few representative…

A: The orthogonal trajectories are the curves that are perpendicular to the family everywhere.

Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,