a. Find the equation of the tangent plane to the level set g(r, y, z) = c at the point P(2,-1, 1) in the level set, and find the value of c. b. Find a unit vector u so that the directional derivative of g at point the P, denoted Duglp, is zero.

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

A: To find the directional derivative of the function at a given point in a unit direction.

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

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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 equation of tangent plane, normal plane and rectifying plane to the curve of the position…

A: The position vector rt=13t3i+3tj+12t2k at t=-1. Then we have to find the tangent plane and normal…

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

A: Answer is mentioned below

Q: Which of the following is the directional derivative of f(r, y) = r'y at the point (-1,-1) in the…

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Q: Find the unit tangent vector and the length of the indicated portion of the curve: (a) r(t) = (6 sin…

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

A: We will find the equation of tangent plane to the given surface.

Q: 5. For a given function f(x, y) = Vx² +y² , what is the directional derivative of f at any point…

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Q: A space curve is given by the vector function r(t) = (3t, t² + 6t, t³ ). Then the unit tangent…

A: GIVEN: r(t) = {3t, t2 + 6t, t3}

Q: Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the…

A: Given the curve     rt=2sin(t),2cos(t),4sin2(t) and the point P1,3,1.

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

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Q: 7. Find the equation of the tangent plane to each surface at the given point. (a) x? + y? + z² = 14…

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Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

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Q: In Exercise nnd the directional derivative ofJ at J at the point P in the indicated direction. f(x,…

A: The given question was taken from the vector calculus in which we have to find the directional…

Q: Find the directional derivative of the following function at the given point P in the direction of…

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Q: (a) Consider the curve C : r(t) = [t , –t², 2– t²]. Find a tangent vector, a unit tangent vector and…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Determine the directional derivative of the following functions in the vector direction specified at…

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Q: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

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

A: Please refer the attached image for complete solution.

Q: Find the unit tangent vector at the indicated point of the vector function r(t)=e^(3t)cos(t)(i) +…

A: Given vector is,

Q: Let f(r.y) = r'y- Find a unit vector tangent to the level curve f(r, y) = 3 at its point (1,2).

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Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

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

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Q: Compute the directional derivatives of the following functions along unit vectors at the indicated…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 6ti – t²j,…

A: To Determine: find the unit tangent vector to the curve at specified value of the parameter r(t)=6t…

Q: Show that if r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies…

A: If r(t) is perpendicular to the tangent vector r′(t) for all t, then the curve r(t) lies on a sphere…

Q: Consider the following. x, y) = 9 + ay² c = 85, P(3, -1) (a) Find the gradient of the function at P.…

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Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

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Q: For the function f(x, y) = 2x² – 3xy + 8y² + 2x – 4y + 4, find a tangent vector to the level curve…

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Q: Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y…

A: Given: Let C be the curve of intersection of the surfaces with equations x2+y=5  and   24x + 4y + z…

Q: Q19:- Find the magnitude of the maximum and minimum directional derivatives of the function w =…

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , e" cos u , e¯º ) at the point where u…

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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 a tangent vector of unit length at the point with the given value of the parameter t. r(t) =…

A: Given, r(t)=(1+t2)i+t2j To find the unit tangent vector at the point t=1.

Q: Given a curve C: r(t), find a tangent vector r' (t), a unit tangent vector u' (t), and the tangent…

A: Given That  A curve C : r(t)=t i^+1tj^ +k^ and P:2,12,0 To Find : Vector r'(t) a unit vector u'(t)…

Q: g(s, t) = 8 vt, (2, 4), v = 2i – j %3D

A: Consider the formula for the directional derivative in the direction of any vector v. First…

Q: Given a curve C: r (t), find a tangent vector r (f), a unit tangent vector u'(t), and the tangent of…

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

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z = y?…

A: Given: The two surface equation: z = y2 and  x2 + y2 = 4

Q: Consider the following. f(x, y) = 9x2 + 4y2 c = 52, P(2, −2) (a) Find the gradient of the function…

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Q: f(x, y) = e2² –3y°, u = (0, 1).

A: The directional derivative of fx, y in the direction of u=a, b is as follows. Dufx, y=fxx, ya+fyx,…

Q: Which of the following is the directional derivative of f(r, y) at the point (0,0) in the direction…

A: Formula to find the directional derivatives helps to find the required directional derivative in the…

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

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Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = (2 -…

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

A: g(s, t) =st(a) The gradient is just the vector of partial derivatives. The partial derivatives of g…

Q: For the function f(x,y)=(4−x^2−y^2)/−5, find a unit tangent vector to the level curve at the point…

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Q: Show that for every point on the curve r(t) = ⟨etcost, etsint, et⟩, the angle between the unit…

A: First we find unit tangent vector any arbitrary point on given curve

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.…

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