In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the point (, 1).

Q: ) Find symmetric equations for the tangent line to the graph of f(r, y) = at (1, 2, 2) in the plane…

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Q: Find the equation of the tangent plane to z = f(x, y) at the point (1, , 1).

A: Given Data: Surface: z=x2esiny Point: x0, y0, z0=1, π, 1   (a) The first derivative of the given…

Q: of Q tind diretion derivative of 2メ×+sin ++ll tnthedirection of vector 3.

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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: Find the equation of the tangent line to sin (x – 2y) = 2xy – 1 2лу — (1.:) at the point ( 1,

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Q: Find equation of tangent line y=4x cos x at the point (π, -4π) y = mx + b where M = and b =

A: To find tangent line .

Q: What is the definition of the directional derivative for afunction of two variables, f (x, y)? Be…

A: Definition of directional derivative of function of two variable.

Q: Find the equation of the tangent line to sin-(x - 2y) = 2xy – 1 %3D (1). at the point

A: Given,            The equation of the line is sin-1x-2y=2xy-1 and the point is 1,12.We know that,…

Q: Find the derivative, r'(t), of the vector function. r(t) = tan(8t), sec(4t),

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Q: Find an equation of the tangent line to the astroid at the (3√3, 1).   x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

Q: What is special about the derivatives of vector functions of con-stant length? Give an example.

A: What is special about the derivatives of vector functions of constant length

Q: Find the derivative of the vector function below r(x ) = sin²(sec.x 2)i +csc³(Vx ² +1) j +8tan(x -k

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

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

A: We have to find the derivative of the given vector function  r(t)=< tan(2t) ,sec(5t) , 1/t^3>…

Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction…

A: Firstly, we calculate unit vector in direction of vector u.

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: Find the equation of the tangent plane to z = In(x²y) – x/ỹ at (-,4).

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Q: Find the equation of the tangent plane to z at (-4,2).

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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 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 equation of the tangent line at the given point on the curve. 2y - Vx = 4. (16,2) y =U

A: We need to find equation of tangent line.

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,…

A: The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

Q: 7(t) =

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Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: Find the equation of the tangent line to the spiral r= x at the point with x=π

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Q: Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in the direction a.…

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Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: ) Find the directions in which the directional derivative of f (x,y) =4x2+sin (5 xy) at (1,0) has…

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Q: Write down the vector equations of the tangent lines to the traces for /(r, 3) = re-y² at (2,0) for…

A: To write the vector equation of the tangent line for the below function to the trace y=0.…

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: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given Data:  Function: fx, y=sin6x+y Unit vector: u=cosθi+sinθj Point: Px, y=P0, π Angle: θ=-5π6

Q: Find the derivative of the vector function below r(x ) = sin°(secx ²)i +csc°(Vx² +1)j +8tan(x -)

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Q: Find the slope of the tangent line to the curve 2 sin(z) +4cos(y) –- 3 sin(z) cos(y) + z = 7x at the…

A: The objective is to find the slope of tangent line to the curve at the point (7π, 3π/2).

Q: find the directional derivative of the function in the direction of the vector v

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Q: Find an equation of the tangent line at the point indicated.

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Q: What is special about the derivatives of vector functions of constant length? Give an example.

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: , (a) Find the directional derivative of at (-2,1) in the direction u = ?-j. X.

A: Since you have asked a different question. I am answering the first one. Please post the question…

Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

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Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: The directional derivative of f(x, y) in the directional

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Q: Find the equation of the tangent line to the curve: sin (2x + y) + cos-'(x +2y) 6 at the point Enter…

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Q: Find the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).

A: This question is related to 3D geometry and equations of plane and lines,  we will solve it using…

Q: Find the second derivative of y with respect to x from the parametric equations given.

A: The objective is to Find the second derivative of y with respect to x from the parametric equations…

Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: . Find an equation of the tangent line to the curve sin(x + y) = 2x – 2y at the point (π, π).

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Q: Find the equation of the tangent plane to z= 6x +2 at the point (1,5).

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