21. For the curve 7(t) = sin ti + cos tj, find 7 '(t) and sketch the position vector 7(÷) and the tangent vector 7 '(4).

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: 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 F(t) = (4 cos(t), 4 sin(t), 3 sin²(t)) at t = 3…

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Q: Q1/Find the tangent and normal vector for curve = (5sin n i+5 cos n j+n k)

A: we have to find the tangent and normal vactor

Q: r(t) = (sin 7t, t, cos t)

A: The vector equation is r(t)=sinπt, t, cosπt. Here, x=sinπt, y=t, z=cosπt Then x=sinπy, and z=cosπy…

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: 2. Find the unit tangent vector for the curve r(t) = (t cost, tsin t).

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Q: 4.a. Find the unit tangent and normal vectors to r(t) = 4 cost i + sin t j at t = /2. Sketch a…

A: Given that rt=4cost i +sin t j Then r't=-4sin t i  +cos t. The formula for tangent vector is…

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t): = 7 cos(t)i…

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Q: For f(x, y) 5æ sin(ry) at the point (3, 5), the direction in which the maximum rate of change occurs…

A: The objective is to find the direction in which maximum rate of change occurs.

Q: At time to, a moving particle has the velocity vector v = 7i and the acceleration vector a = 7i +…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: 0. for the funchion f (x,4) = 3-x?- u?, find a unit tangent vector to the level curve at the point…

A: Given: fx,y=3-x2-y2-3 at P3,5​​​​​​​

Q: Sketch the curve parametrized by r(f) = (1 – 12, 1) for -1sı<1. Compute the tangent vector at i = 1…

A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

Q: Q1/Find the tangent and normal vector for curve (5sin n i+5 cos n j+n k)

A: We have given r(t) and we have to find tangent and normal vector to r(t)

Q: Let x(t) be a Bézier curve and the tangent vector x' (t) is computed. What does knowing that x'(0) =…

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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 curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. .…

A: Given:                  rt=cos3tj+sin3tk,     0≤t≤π2                 v=ddtrt=ddtcos3t j+sin3t…

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: How would I find the unit tangent vector T(t) at the point with the given value of the parameter t.

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Q: Find the unit tangent vector of the curve: 7(t) = (3 cos t , 3 sint, t2) at t = 0. %3D

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Q: 7) Find the unit tangent vector for the parameterized curve: r(t) = cos ti+ sin tj+ sin tk, 0≤t< 2π

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Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

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: 3. A unit vector tangent to the curve y x2 at the point (2, 4).

A: We are entitled to solve only one question at a time so we will answer only the first question.…

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t))i + (5 sin(6t)) j +…

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

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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 a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make…

A: Given that, y=x3   We have to find a unit vector parallel to the tangent line of the given curve at…

Q: Find the unit tangent vector to the curve defined by 7 r(t) = (5 cos(t), 5 sin(t), 2 sin² (t)) at t…

A: To find the unit tangent vector to the curve defined by r→t=5 cost, 5 sint, 2 sin2t

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

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Q: Find the unit vector towards the tangent of the curve y = x at x =1

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

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

Q: Let the the position vecor be R(t) = (e' cos(3t) , e' sin(3t),0). Compute the unit tangent vector

A: The given position vector is R(t)=etcos(3t),etsin(3t),0 . compute the unit tangent vector T(t)=?

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

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Q: For f(z, y) is: = 5a sin(xy) at the point (2, 4), the direction in which the maximum rate of change…

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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 unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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

A: Consider the given function, fx,y=4e4xsiny now, find the partial derivatives,…

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

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Q: Compute the unit binormal vector and torsion of the curve r(t) = (8t, 5 cost, 5 sint (5, 8 sint, -8…

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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: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

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Q: We start by finding the tangent vector to the curve. For r(t) = (10t, 3 cos(t), 3 sin(t)), we have…

A: Given rt=10t ,3cost ,3sint

Q: Find the unit tangent vector to the curve r(t) = (2sin(t),2cos(t)) at the points t =-n, t=0 and t…

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

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