Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t) defining the curve.

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point…

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Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: 1. f(x, y) = 1+ 2x/y, (3,4), v= 4î – 3ĵ |

A: According to our company policy we can answer only first question and rest can be reposted. Thanks

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

A: The objective of the question is evaluate the directional derivative at the given point and…

Q: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Find the directional derivative of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

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Q: The three components of the derivative of the vector-valued function u are positive at t = t0.…

A: Given: The three components of the derivative of the vector-valued function u are positive at t =…

Q: Find a vector-valued function whose graph is the indicated surface.

A: Given : The plane x + y + z = 6.   To find a vector-valued function.

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: : Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² + 2y²…

A: To find the directional derivative of the given function.

Q: Represent the plane curve by a vector-valued function. y = (x − 2)2

A: y=x-22 Now let xt=t Now put xt=t in y=x-22, we get y=t-22

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Givenf(x,y)=xx2+y2 , (2,1) , v=<3,5>

Q: Find the directional derivative of the function f(x,y, z) = V22+ y² + z² at point (2, -3, 6) in the…

A: In this question, we want to find the directional derivative of the given function at given point…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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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: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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Q: 3. A unit vector tangent to the curve y x2 at the point (2, 4).

A: We are entitled to solve only one question at a time so we will answer only the first question.…

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 directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: 2. Find the equation of the normal line and the tangent to the parametric surface defined by the…

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Q: Find the unit vector towards the tangent of the curve y = x at x =1

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the…

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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

Q: Find the directional derivative of the function f(x, y, z) = /ryz at the point P(2,2, 2) in the…

A: Topic-vector calculas

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

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: (b)Find the directional derivative of f(x,y,z) = x²y- yz3 + z %3D at point (1,-2,0) in the direction…

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Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

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Q: Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the…

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Q: Find the directional derivative of the function f(r,y) In(z +y") at the point (2, direction of the…

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Q: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function f(x, y, z)=(x3-xy2-z).........(1) We have to find the derivative of the function…

Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

Q: If f (x, y, z) = xy + xz + yz, find this function's directional derivative at (-1,3,5) in the…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Given: Function f(x, y, z) = x2y + y2z , point (1, 5, 6) and vector v = <2, -1, 2> To Find:…

Q: Find the directional derivative of f(x,y,z) = x²z – xz³ + zy at the point (1, -2,0)in the direction…

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Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: Find a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2…

A: To determine the vector function for the curve of intersection between the surfaces.

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

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Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.

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,

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.