a) Start by finding a single vector function that represents the intersection of the surfaces z = y? and x? + y² = 4. Use that vector function to sketch the curve from 0

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

A: In polar coordinates, Using this rule, using appropriate substitutions:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

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Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? + z? = 25 at the point…

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Q: Sketch the graph of the plane curve . r(t) = ti − t3j and sketch the vectorsT(t) and N(t) at the…

A: Here we are taking the T(t) as the tangent vector and N(t) as the Normal vector Consider the…

Q: Sketch the space curve represented by the vectorvalued function                  r(t) = ti + (2t −…

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Q: Find the equation of the tangent plane at the point T(1,1,4) of the sphere (x – 1)2 + (y – 2)² + (z…

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Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y? + Z?…

A: We need to identify a generating curve on the xz-plane for the surface of the revolution with the…

Q: Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

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Q: Find the equation of the tangent plane to the surface z = at the point (2,-3, 10) O r- 6y – z = 10…

A: We have to find the equation of tangent plane.

Q: Consider the curve defined as r(t) = e^ti + e^tj + t k Determine the point on the curve where the…

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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 equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

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Q: Find a vector function that represents the curve of the intersection of the two surfaces. The…

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Q: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

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Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

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Q: Find a vector function that represents the curve of intersection of the two surfaces. The paraboloid…

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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: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

A:

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane  will be…

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

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: V7x + 2y – x = y.

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Q: Find an equation of the tangent plane to the surface 2² + 2y? + z? = 175 at the point (5, -5, 10).

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Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

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Q: Write an equation for the plane tangent to the surface F(x, y, z) = 0 at the point (a, b, c).

A: Given surface is Fx, y, z=0 and the point is a, b, c.

Q: Find the value of a at which the plane curve traced out by the vector function E + bt> is not…

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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: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: We have to find vector function For this we have given equation of paraboloid and parabolic cylinder…

Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: First solve the given equations for finding the values in terms of x

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A: The objective is to find the vector function that represents the curve of intersection of the two…

Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

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Q: Find the equation of the plane tangent to the surface z x+y at the point (2, 1, 3). x-1

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Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = < -2, 5, 4>     ---(1)  B(t) = < 3/5 cos t , 3/5 sin t , 4/5 >    => B(0)  =…

Q: ind a formula for a vector normal to the plane tangent to f(x,y) at (xo, Yo).

A:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

Q: What is the perpendicular vector to the surface f(x.y.a)-ay-3r+'y-0 at (1,-1,2)? (3,3.0) (1,1.3)…

A: A vector that makes an angle of 90 degrees with the given surface is said to be perpendicular to the…

Q: Sketch the plane curve. r(t) = 2ti-tj, [0, 2] y -1 y 2 1 Find its length over the given interval. 2…

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Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? +z? = 25 at the point…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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