Find a tangent vector at t= In 2 for the following parameterized curve. r(t) = 5 e'i+e -2tj+6 e 2k Choose the correct answer below. O A. 5 In 2i- 2 In 4j + 12 In 4k O B. 10i -j+48k OC. 5i-2j + 6k O D. Since r'(t) = 0, there is no tangent vector.

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Q: Find a parametrization of the tangent line at the point indicated.

A: r(s)=(ln s)i+s-1 j+9sk;s=1

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A: We have to find tangential component and normal component

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A: Solved below.

Q: A bee with velocity vector r' (t) starts out at (3, –5, –2) at t = 0 and flies around for 3 seconds.…

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Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

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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

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Q: Find the tangential and normal components of acceleration at the given time t = 1 for the space…

A: Given rt→=ti^+2tj^-3tk^t=1

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Q: YouTrylt 4 Consider the path of a particle given by tangential and normal components of acceleration…

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Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Let c(1) be a path and T the unit tangent vector. What is / T- ds? c'(1) The arc length of e. The…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: 10. Find the unit tangent vector to the curve below at t=r/3 r(t)=sin ti+Cos tj+tan tk

A: We have to find the unit tangent vector to the curve at t=pi/3.    r(t)= sin2ti + cos2tj + tan2tk .

Q: Find a tangent vector at t=, for the following parameterized curve. 2 r(t) = (t, sin 6t,7 cos t)…

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Q: Consider the parametric curve: x = ln(t + 5) y = −6t5 Which integral gives the arc length of the…

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Q: If r(t) = cos(2t)i + sin(2t)j – 4tk, compute the tangential and normal components of the…

A: Given:- rt=cos2ti+sin2tj-4tk Find Tangential and normal component of acceleration vector

Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

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Q: Find the tangential and normal components of acceleration at the given time t for the plane curve…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) = (1 - t4, 4t, 5t), t = 2…

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Q: Find a tangent vector at t= for the following parameterized curve. r(t) = (5t, sin 6t,3 cos t)…

A: Recall: Tangent vector to the given curve r(t)  is r'(t).

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Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

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Q: 3. Find the arc length traced out by the endpoint of the vector-valued function 1 †(t) = t cos t î +…

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Q: 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.

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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: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: Find the unit tangent vector T and the principal unit normal vector N for the following…

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Q: A bee with velocity vector r' (t) starts out at (2, 5, -2) at t = 0 and flies around for 1 seconds.…

A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

Q: Consider a curve C in guen by r(t) = / 7t-Sin(F) cas(t), 4t, -2cos (+)) with Oste5 Verify that ri(t)…

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Q: 4. Consider the closed curve C, which is the image of the path 7(t) = (a cos t, b sin t), t E [0,…

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Q: . Compute the tangential and normal components and express the acceleration a in the form a =…

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A: Explained below

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