The velocity components in the x and y directions in terms of stream function w is given by

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: Obtain the gradient to a curve with parametnic equations given by and y= X= In 2 2t when t-1

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Q: In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the %3D…

A: We have to find maximum directional derivative.

Q: For f(x, y) 5æ sin(ry) at the point (3, 5), the direction in which the maximum rate of change occurs…

A: The objective is to find the direction in which maximum rate of change occurs.

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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Q: Two ships A and B are moving northeast with peed VA=22 knots, and west with speed VB= 19 knots,…

A: Given: VA=22 knots in northeast VB= 19 knots in west To find: Relative velocity of A with respect to…

Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

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Q: Find the directions in which the directional derivative of f (x, y) = ye*y at the point (0,2) has…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Find the equations of the tangent plane and the normal line at point (1,1,-2) to surface z^2 =…

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

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Q: Find equations of (a) the tangent plane and (b) the normal line to the surface 2(x−2)^2 + (y−1)^2 +…

A: Given surface is Firstly, we find all first order partial derivatives At point (3,3,5)

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find the gradient of the function w = xy2z2,  and the maximum value of the directional derivative at…

A: Given function:    w=xy2z2

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point (1,3)…

Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: (a) Find the directional derivative of f(z, y) = ry + y at the point (1,2) in the direction (1,1)

A: Solution a: Given function is f(x, y)=xy+y Now gradient of the function is ∆f(x, y)=∂f∂x, ∂f∂y⇒∆f(x,…

Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: Find the directions in which the directional derivative of f(x, y) = ye at the poist (0, 2) has the…

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Q: A DVD has a diameter of 4.75 in. and rotates at 360.r/min. What is the linear velocity of a point on…

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Q: Calculate the directional derivative of f(x,y)= In( Vx +y ) at point (1,1) in the %3D direction of v…

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Q: =) Find the directional derivative at the point P = (2, 1, 1) of the scalar function in the…

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Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: According to the given information, it is required to find the maximum rate of change of f at the…

Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: Find an equation of the normal line to the surface z = ye 2æy at the point (0, 2, 2).

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: Consider the level curves for F (x, y) = x² – y². y (a) How do we sketch in the gradient vectors?…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: If f(x, y) = xy, find the gradient vector Vf(7, 5) and use it to find the tangent line to the level…

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Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

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Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: Consider the unsteady flow u= u0, v = kt, w = 0 where uo and k are positive constants. Show that the…

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Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: Let f(x,y,z)=xyz. What is the directional derivative of f in the direction of the unit vector…

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Q: ) Compute the directional derivative of f(x, y) = x2 y at the point (1, 1) in a direction normal to…

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Q: Find the derivative of f(x, y) = e*y + eY at the point (1,3) in the direction of the vector

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: are two linearly independer d'y 3dy equation dx? dx

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Q: Determine dyðx Calculate the instantaneous rate of change of g at the point (4,1,2) in the direction…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: Let f ( x , y ) = 2 x − y + x2 + y4. Which (unit) direction vector u  MINIMIZES the directional…

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Q: Let f(x, y) = x /G. At the point (1, 4), find a vector (a) In the direction of maximum rate of…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.