Given a curve C: r (t), find a tangent vector r (f), a unit tangent vector u'(t), and the tangent of C at P. Sketch curve and tangent. 24. r(t) = [t, 31?, 1], P: (2, 2, 1)

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: For the curve defined by F(t) = (e-t, 3t, e') find the unit tangent vector, unit normal vector,…

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Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 2 sin? (t)) at t =…

A: Find the unit tangent vector to the  curve defined byr→t=4cost, 4 si t, 2 sin2tat t=π.T→π=…

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 the equation of the tangent plane to z=e^y+x+x^5+10   at the point (3,0,257)

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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: For the following parameterized curve, find the unit tangent vector. r(t) = (e",2 e" 2 e-8t), for…

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Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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Q: 3. Find the curve's unit tangent vector and find the length of the indicated portion of the curve:…

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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: For the curve defined by 7(t) = (e* cos(t), eʻ sin(t)) find the unit tangent vector, unit normal…

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Q: For the following parameterized curve, find the unit tangent vector. r(t) = (e 2",2 e 2",2 e 31),…

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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 equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

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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: Q.7: (A) Find the unit vector towards the tangent of the curve y = x at x =1

A: Find the unit vector towards tangent of the curve y=x2 at x=1.

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

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Q: For the curve defined by F(t) = (e¯', 4t, e') find the unit tangent vector, unit normal vector,…

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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: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

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Q: or the following parameterized curve, find the unit tangent vector. r(t) = (e ",3 e ",3 e -71), for…

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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 T(t) to the curve r(t) 2 = (, sint – t cos t, cos t +t sint), t> 0,

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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: Find the unit tangent vector (t) at the point with the given value of the parameter.. r(t) = (4te,…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. (₁)-[ = T T r(t)…

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Q: Find the unit tangent vector to r(t) = (t2, tan−1 t,t) at t = 1.

A: To find the unit tangent vector to rt=t2,tan-1t, t at t=1. Solution: The unit tangent vector is the…

Q: For the curve defined by 7(t) = (e-, 3t, e') find the unit tangent vector, unit normal vector,…

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Q: For the curve 7 (t) = (F + 1) 7 + (3t – 4) j+ ( – 1)E. Find the unit tangent vector to the curve at…

A: Given:             r→t=t2+1i^+3t-4j^+t2-1k^ Find: v(t)            vt=r't=2ti^+3j^+2tk^ and…

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: Next Consider the two vector-valued functions given by r(t) = (t+1, cos 1+t w(+) = (*, sin() *) . a.…

A: (a) The two vector valued functions intersect if r(a) = w(b) for some t = a and s = b.…

Q: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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Q: For the curve defined by →r(t)=⟨e^−t,4t,e^t> find the unit tangent vector, unit normal vector,…

A: We have to find the unit tangent vector, unit normal vector, normal acceleration, and tangential…

Q: - 5x2 + xy + 5y? + 5x + 4y +3, find a unit tangent vector to the level For the function f(x, y)…

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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: Find the unit tangent vector to the curve defined by F(t) = ( 5t, V36 – t2) at t = 1. T(1)

A: Given: r→t=-4t,-5t,36-t2 at t=1 We have to find the value of 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: How do you find the Unit Tangent Vector to a curve C when you are given x(t) and y(t)? Where you are…

A: Suppose we are given a smooth curve C:r(t)→=<x(t),y(t)>on an openinterval I. Then a unit…

Q: For the function f(x, y) = 3x – 5xy + 4y – x + 4y – 2, find a unit tangent vector to the level curve…

A: Gradient of  function: Let z=f(x,y)z=f(x,y) be a function such that  partial derivating of with…

Q: Find the vector equation of the tangent line to F(t) = 2 (e-) in t i+ tan-tj+ the point where t = 1.…

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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: The tangent vector to a curve r is given by r′(t)=⟨16t,128t^2,1⟩. Let T be the unit tangent vector.…

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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: 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: 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: For the curve defined by F(t) = (e- cos(t), e' sin(t)) %3D find the unit tangent vector, unit normal…

A: According to our guidelines we can answer only first three subparts Given curve defined by r(t)=…