1. Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point (7,,0). 2. Evaluateſff, y dV, where: E = {(x,y, z) | 0

Q: 8. The second directional derivative of a function f(r, y) is DS(x, v) = D.[D.f(r, y)]. If f(r, y) =…

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Q: An equation of the tangent plane to the surface 1+y z = at the point p(1, 3, 2) is 1+x (A) (x-1) -…

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Q: In Exercises 1–5, find equations for the (a) tangent plane and (b) normal line at the point P0 on…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: If the gradient of f is ∇f=y3j−xi+zyk and the point P=(−8,6,2) lies on the level surface f(x,y,z)=0,…

A: To find the equation

Q: Find an equation for the tangent plane to cos(rx) – x²y+ e*z + yz = -4 at the point (0, 1, –6). = 0.…

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Q: Find an equation of the tangent plane to the given surface at the specified point. f(x, y) = tan xy.…

A: From the partial derivative with respect to x and with respect to y

Q: 03. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9,…

A: the surface is fx,y the gradient to the surface at (1,1) is ∇fx,y Let the value of the gradient is…

Q: Q9. Find the equation of the tangent plane to f(x, y) = x ln(y) +x²y+3 at the point (x, y) = (2, 1).…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) 12x…

A: Given equation of the surface  xyz=12 Point on the surface is 1,3,4 (a) Find equation of tangent…

Q: Vy: y(0) = 1 dx dy Vy: y(0) = 0 %3D %3D dx dy - x-y; y(2) = 2 %3D dx dy VX-y; y(2) = 1 %3D dx

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 4, 5) (b)…

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Q: 2. Show that f(t) =1 – sint defines a smooth flow on the manifold S = ( (cost,sint) ), but %3D g(t)…

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Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, x + 3z, 2x + 3y). (b) If C is the curve…

A: Let the function f(x, y, z) = xy + 2xz + 3yz which satisfies the given property  Gradient (f) = ( y…

Q: Find the equation of the tangent plane to the surface z = ln (2x + y) at the point (-1,3,0) .…

A: To find the equation of the tangent plane to the surface z=ln2x+y at the point -1, 3, 0.

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 8, (1, 2, 4) (b)…

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Q: If the gradient of f is Vƒ = 3x i + z² j+ 2yz k and the point P = (4, –6, –9) lies on the level…

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Q: Let g(x,y,z)=5xe^y+yz^2. Use the gradient vector to find the equation of the tangent plane to the…

A: Solve the following

Q: Calculate the gradient of the tangent to the following curves at the given 1 y = 3x', x = 1 y = 2x –…

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Q: Find and equation of a) the tangent plane and b) the normal line to the given surface at the…

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Q: A table of values of a function f with continuous gradient is given. Find Vf dr, where C has the…

A: at t = 0, x=02+1 =1 , y=03+0=0  ⇒ Point is (1,0) at t = 1, x=12+1=2,  y=13+1=2 ⇒Point is (2,2)

Q: Solve Laplace's equation u +u, = 0, 0<x< 5, 0 < y< 4_for a rectangular plate %3D subject to the…

A: Laplace equation: uxx+uyy=0 For a rectangular plate 0≤x≤a, 0≤y≤b With boundary conditions: u(0,y)=0,…

Q: Q3: For the surface f (x, y, z) = In (xyz), find: (1) the gradient of f at (1,1,2), (2) the…

A: Given

Q: Q1. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9,…

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Q: 1) Let f ( x , y ) = x 2 + 6 x y + y 3. Find all points (x,y) where ∇ f ( x , y ) = 0.

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

Q: 1. Find the gradient of the following functions at the given point and hence find the directional…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If the gradient of f is ∇f=yj⃗ −xi⃗ −4zyk⃗  and the point P=(−7,−8,−3) lies on the level surface…

A: an equation for the tangent plane to the surface at the point P

Q: Q. A-Find the gradient (Vf) for the following level surface at the given point: f(x, y, = x2 + y² -…

A: Given: f(x,y,z)= x2+y2-2z2+zlnx  Gradient,∇f=i∂f∂x+j∂f∂y+k∂f∂z

Q: 1. Fad the equation of the tangent plane and normal line to the surface z = 2r+y at the point…

A: Given that z=2x2+y2. We need to find the equation of the tangent plane and the normal line to the…

Q: Letf(x,y,z) = x^2+y^2+z^2.  Calculate the gradient of f.  Calculate ∫_C(Fdr)  where F(x,y,z)=(x,y,z)…

A: Given  f(x,y,z) =x2+y2+z2

Q: If the gradient of f is Vf = yj – z i+ 2xy k and the point P = (-3, 7, 8) lies on the level surface…

A: We have to find an equation for the tangent plane to the surface at the point P(-3, 7,8).

Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, æ + 3z, 2x + 3y) (b) If C' is the curve…

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Q: 13. J(L, Y) y", 1(-1, 1) = 8 – 2x2 – y². For the following level curves f(x, y) = C and 50-51. Level…

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Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: Let f (x, y, z) = ln (1+x³ + y* + z®) Find an equation for the tangent plane to the surface f (x, y,…

A: We have to find the tangent and normal line equation .

Q: Find an equation of the tangent plane to the surface z = In(2x + y) at the point P(-1,3, 0) Select…

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Q: A table of values of a function f with continuous gradient is given. y012 Find x 1 2 38 2 1 5 7 9 4…

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Q: i+ (x-my)j + zx*k and f=w0 0 cos "(yz - y²) xy If w In + m find at point (-m,0,2): (1) the…

A: We are provided with functions: w=lnxy-1y2+mi+zx-myj+zx2kf=w·cos-1yz-y2zk The objectives are at the…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 4, 3) (b)…

A: Given xyz=12 Point is (1,4,3) To find: equation of the tangent plane to the surface at that point…

Q: If the gradient of f is Vf = x? j – z i+ 3yx k and the point P = (-4, 3, 1) lies on the level…

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Q: Please work out the results of the following differential operations • Gradient of f (x, y, z) = x²…

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Q: 5. Let u(x) be a differentiable function with u(1) = 2 and u'(1) = 3. Find an %3D equation of the…

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Q: 2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next,…

A: Given the velocity is u=αx, v=-αy, w=0 and Lagrangian description is x=Xeαt, y=Yeαt, z=Z

Q: If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an…

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Q: Consider the following. xy + yz + zx = 17, (1, 1, 8) (a) Find an equation of the tangent plane to…

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Q: Consider the following. Z = =DVx²+ y?, 5x - 2y + 3z = 22, (3, 4, 5) (a) Find symmetric equations of…

A: a) Here, f(x,y,z)≡x2+y2-z2=0g(x,y,z)≡5x-2y+3z=22P≡(3,4,5)

Q: 8. Consider the surface S of equation z2-2x? + y²-x= 0 and let P (2, 3, 1) be a point at S. Suppose…

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Q: For the given surface f (x, y) = 2 + sin(xy) at the point (1, 0, 2), find the following: a) Gradient…

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Q: 1. Determine the directional derivative of the surface f(x, y) = 3x? + y³ at the point P(1,2) in the…

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Q: 2. Show that f(t) = 1 – sint defines a smooth flow on the manifold S = ( (cost, sint) ), but g(t) =t…

A: The given question can be solved as shown in step2

Q: 40. (a) Let f(x, y, z) = x2 + y2 − xyz. Find grad f. (b) Find the equation for the tangent plane to…

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