Consider the function f(x,y) = 3x*-xy+2y +4 and the point P(- 1,2). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P.

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Q: 8. Given the function g(x, y, z) = x²y - 4zex+y, find the slope at P(1,0,1) in the direction of the…

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Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

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A: So we have;

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Q: The divergence of the vector F = a²yî + æyz} – a*y°k is x2 y? k is -

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A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

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Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

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Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

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A: Solved below

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Q: (b) Identify the unit vector u pointing in the direction of maximum increase of the function f(x, y)…

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Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: Represent the plane curve by a vector-valued function. 2x − 3y + 5 = 0

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x² + y? = 2 and y? + z² = 2…

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Q: Represent the plane curve by a vector-valued function. x2 + y2 = 25

A: It is given that, x2 + y2 = 25. Let x=5cost and y=sint , Then 5cost2+5sint2=25cos2t+sin2t=25

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Q: Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

A: Given Fx,y,z=xyey-z2x and P1,0,-1Vector u=⟨2,-3,6⟩

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Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.

Q: Match the vector-valued function with its graph. r(u, v) = ui + vj + uvk -2-1 2 2

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A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (b) Identify the unit vector ū pointing in the direction of maximum increase of the function f(x, y)…

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Q: Find the dircctional deriu atrue Du f(-3,-1,3) for the function f Cxiy,2) =xy + yz +ZX in the…

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Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: Find the point on the graph of z = 2x^2 − 3y^2 at which vector n=⟨8,−12,1⟩ is normal to the tangent…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

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Q: (a) f(r, y) = xª – x²y+y² +6 at P(-1,1) (b) f(r, y) = 2 sin(2x – 3y) at P(0, 7)

A: Please see the explanation below

Q: Consider the function f(x,y) = 5x2 - 2y2 - 7 and the point (2,- 1). a. Find the unit vectors that…

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Q: The gradient vector of the function f(x, y) = 2+ Ty at the point (1, 1) is %3D Select one: O True O…

A: The gradient vector of function f is given by: ∇f=∂f∂x,∂f∂y Here, ∂f∂x=12xyy=y2xy∂f∂x=12xyx=x2xy

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Q: Prove that the vector T'(t) = 0 for moving in a straight line

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Q: Let ƒ(x,y) = x²e"9. Give the unit vector that points in the direction of maximum increase along the…

A: Given that: f(x,y)=x2exy&amp; the point is (x,y)=(1,1)

Q: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (2,-2, 5), b (2,-5, 3),…

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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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Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3…

A: Given vector function is,