3. Find the curve's unit tangent vector and find the length of the indicated portion of the curve: r(t) = (2 + t)i - (t + 1)j + tk, 0<1<3

Q: Find the unit tangent vector to the curve at the specified value of the parameter.

A: Given vector is rt=5cost i+5 sint j. To find the unit tangent vector to the curve at t=π3. Solution:…

Q: What is the unit tangent vector to the curve r(r)=sint i+2cost j when t=π/4

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

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Q: Find the unit tangent vector to the curve defined by T(t) = (- 3t, 5t, V100 t) at t = 7. T (7) =

A: The given vector is: r→(t)=-3t, 5t, 100-t2

Q: Find unit tangent vector of the curve r=(2+t)i-(t+1)j+k

A: In this question, we need to find the unit tangent vector of the given curve.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y2, (12,…

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Q: Find the set of parametric equations for the tangent line to the graph of the vector-valued function…

A: To find the set of parametric equations for the tangent line to the R(t)=&lt;t+sin3t, t+cos3t,…

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: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

A: (1) Given curve r(t)=t3i+2t2j,  t=3. (2) r(t)=6cos(t)i+6sin(t)j,  t=π3 The objective is to find the…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (12,…

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Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

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Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

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Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

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

A: The given space curve rt=e2ti+cost j - sin3t k. Its derivative is r't=2e2ti-sint j - 3cos3t k. At…

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

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Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: Find the unit tangent vector to the curve defined by 7(t) = (5 cos(t), 5 sin(t), 4 sin (t)) at t = 3…

A: We find unit tangent vector of given curve at t=π/3

Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

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

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Q: Find the unit tangent vector to the curve at the specified value of the parameter           r(t) =…

A: Given :  The the vector r (t) = 6t i→ - t2 j→   and the parameter t = 2.   To determine : The unit…

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: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: Find the unit tangent vector of the given curve. r(t) = 12t5i - 4t5j + 3t°k %3D

A: Given the vector function, r(t) , we call r′(t) the tangent vector provided it exists and provided…

Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find the unit tangent vector to the curve defined by F(t) = (5t, 2t, V16 – t) at t = – 1. T(– 1) =

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Q: Find the equation of the tangent plane to z=e^y+x+x^2+1 at the point (5,0,32). z=?

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Q: Show that the vector-valued function r(t) = ti + 2t cos tj + 2t sin tk lies on the cone 4x2 = y2 +…

A: Given: Vector-valued function: r(t)=ti^+2tcostj^+2tsintk^ Cone: 4x2=y2+z2

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: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…

Q: Find the unit tangent vector at t = 0 for the parameterized curver(t) if r'(t) = ⟨et + 5, sin t + 2,…

A: Given: r't=et+5,sint+2,cost+2 The unit tangent vector to a curve rt can be calculated as,…

Q: Find the unit tangent vector to the curve defined by r(t) = /16 – t² ) at t = (- 4t, – 3t, T(- 2) =

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Q: find unit tangent vector of the given curve r(t)=(4-2t)i+(2t-3)j+(8+t^2)k

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = ti + 8t2j,…

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Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: Find the equation of the tangent plane to z = e² + y+ y*+3 at the point (0, 5, 634).

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Q: Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).

A: We have given equation z=x2+y2 First we rearrange the equation of the surface into the form fx,y,z=0…

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

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

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