Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = 4√ti + 3t²j + 3tk, t=1 T(1) =

Q: Consider the following parametric curve r(t) =

A: Let rt be the parametric equation of the curve. To calculate the unit tangent vector, use the…

Q: Which of the following integrals has an integrand that is a proper fraction? 2x5 -x + 4x3 -3x2-5x+4…

A: Proper fraction is the sum of partial fractions, The give integral have factors in the denominator…

Q: Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

A: If  is vector valued function which is differentiable and then the unit tangent of is given by

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: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: Motion around a circle of radius a is described by the 2D vector-valued function r(t) = ⟨a cos(t), a…

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Q: Let r(t) = (15, cos t, -3 sint) be the position vector of an object. Find the velocity and speed of…

A: Given that rt=15,cost,-3sint  find the velocity and speed of the object

Q: Let r(t)=(10 cos(t), 1, 10 sin(t)). Find the unit tangent vector u drawn to point P=(6,1,8). Sketch…

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Q: The parametric equation of the tangent line to the curve associated to f(t) = (3t², ²/7 , t + 3) at…

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Q: Consider r(t) = (2t, 3 sint, 3 cost). a. Find the equation of the tangent line to the curve at the…

A: The given position vector is, r(t)=2t,3sint,3cost. (a) To Find: The equation of tangent line to the…