Find an equation for the tangent plane to cos(rx) – x²y+ e*z + yz = -4 at the point (0, 1, –6). = 0. Find equations for the normal line to the surface through that point. x(t) = %3D y(t) = %3D z(t) =

Q: Find the function "y" that makes the integral stationary V1+y²y2

A: Please check step 2 for solution

Q: Write the differential dw in terms of the differentials of the independent variables. w = f(x,y,z) =…

A: Hair we have to find out the differentials

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: Determine the total differential (dg), and total derivative with respect to x 3x 2y g f(x, y, z) 3D…

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Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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

A: Consider the equation of the form          F(x,y,z) =0 then the equation of the tangent plane to the…

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (b) Reparametrize R using…

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Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: find the differential of each function

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Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

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

Q: L{t}(s) = / t dt te -at %3D

A: Here we use integration by parts.

Q: b) Find equations for the tangent plane and normal line at the point po on the given surface.…

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Q: Write the differential dw for the function w = ƒ(x, y, z).

A: Consider the given function w=fx,y,z

Q: Find the linearization L(x,y) of the function f(x,y) = e (X cos (5y) at the points (0,0) and 0,- 2

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Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

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Q: find the decomposition of a(t) into tangential and normal components at the point indicated, as in…

A: Given: r(t)=(t,cost,sint)t=π2

Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

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Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

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Q: The solution of Laplace equation d'u = 0, where 0 < x < 3 dx? and 0 < y < 2 with boundary conditions…

A: Step:-1 Since we know for Laplace equation if step size h= k then ui, j=14ui+1, j + ui-1, j + ui,…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: a particle moves along a curve x = t^3+1, y=t^2, z=2t+5 , where t represents the time . its velocity…

A: Velocity is obtained by differentiating the position function

Q: Evaluate the line integral (2x + 6)dx + (5y+ x)dy along the curve C: C F(t) = tỉ + 2tj, 0<t<1.

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Q: Find the equation for the Tangent Plane on the given surface coS ax – x²y + e*z+ yz = 4 Po(0, 1, 2)

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Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

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Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

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Q: Let y = f(x), where 3x? f(x) : Зx + 4 ,2 x + 4 Find the differential of the function. dy =

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Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: Compute the plane tangent to the graphs at the indicated points using the given functions. (Let z be…

A: Note : As per the authoring guidelines, when multiple subparts are posted, only first 3 subparts or…

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = tan-1 (xyz) at…

A: To find the linearization Lx,y,z of the function fx,y,z=tan-1xyz at 1,0,0

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: r(t) = (2 cos t) i + (t - 3 sin t) j+ ( e) k, t=0 What is the standard parameterization for the…

A: Here rt=2costi+t4-3sintj+e3tk where t0=0 The standard parameterization for the tangent line is…

Q: Write the differential dw in terms of the differentials of the independent variables. w =…

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Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

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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: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).