nd the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter your answer using interval notation.) r(t) = 9t°i – t3j

Q: PARAMETRIZED, VECTOR, VECTORS, MULTIVARIABLE CALCULUS NEED ALL WORK SHOWN CLEARLY AND ANSWERS

A: Given: r(t) = <3e^3t, sint, 3t^2-6t>

Q: Find the derivative of the vector function r(t) = ln(19 - t²)i + √17+tj − 7e-¹t k - r' (t) = (¯¯

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Q: 12. r(t) =t i+t* j at t=1

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

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Q: 1. Consider the vector-valued function Ř(t) = (t³ + 2, –2t³ + 1, – 2t³ + 3). 1.1 Reparametrize R(t)…

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Q: 2. For the vector-valued functions given by 7(t) = i- j+ In t k and ü(t) = t?i – 2tĵ + k Find

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Q: Find the derivative of the vector function r(t) = In(18 – 12) i+ v5+tj- 9e“ k r' (t) = (

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Q: Find the second derivative of the vector-valued function 7(t) = (7t + 4 sin(t))i + (2t + 4 cos(t))3…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: Find the domain of the following vector-valued function. r(t) = sin 5ti + ²√² + ¹ k e

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: 8. D is a curve that is represented by the vector function H(t) =< t² + 5,1 – 4t,; A. Determine an…

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Q: 5. Consider the vector function F(t) = (9 – - 2t, 4+ 2t, v2t² ) (a) Find the arc length of the curve…

A: Solution is here

Q: Find the domain of the vector-valued function r(t) = ln ti − et j − tk

A: Given function is r(t)= ln(t) i - etj -tk

Q: Find the unit tangent vector of the given curve. r(t) = (7- 2t)i + (2t - 3)j + (6 + t)k 2 1 O A.…

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Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

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Q: Find the tangential and normal components of the acceleration vector for the curve F(t) = ( – 3t, –…

A: The solution is given below:

Q: 5. Consider the vector function F(t) = (9 – 2t, 4 + 2t, /2t² ) (a) Find the arc length of the curve…

A: Given that r→t=9-2t,4+2t,2t2. (a) The objective is to find an arc length of the curve on 0≤t≤1. The…

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Q: Fnd the orthogonal trajectorie of the family of curve r = c sin0

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Q: apply linearity property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: f(t)=t cos 2tf(t)=t2 e-3t

Q: x-1_y-2_z-1 -6 (c) show that the line 2 7 curve F(t) = (21+²) 1+ ²+ (in ²²-3) 1+1√21³²-1k at 1=1 i+…

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: 2x + y + z = 1. 7. Find the tangent vector r' (t) and unit tangent vector T(t) at the point with t =…

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Q: Find the second derivative of the vector-valued function →r(t)=(5t+7sin(t))i+(7t+2cos(t))

A: Given that: r(t)=(5t+7sin t)i+(7t+2cos t)j

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If R(0) = (-1,4,-5),…

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Q: Find the derivative of the vector function r(t) = In(10 – t) i+ v10+tj+ 8e-8* k r'(t) = (

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: Q14 Suppose that C is the graph of a smooth vector-valued function r(s) parametrized by arc length…

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth r(t) =…

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Q: Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk…

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Q: Q19:- Find the magnitude of the maximum and minimum directional derivatives of the function w =…

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Q: Q2) Find the vectors „N of the curve r(1) = ) at the point (1.1)

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Q: A. Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1…

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Q: t3 1. Find the vector equation of the tangent line to 7(t) = 2 (e1-t) In t i+ tan-1 tj+ k at cos(t…

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Q: 6. Consider the vector-valued function f: R → R³ given by: f(t) = t/ 4t2 + 1, sin(t) cos²(t), for t…

A: a) f(t)=t4t2+1,sintcos2t,2t2+1we know that f(t)=f1,f2,f3⇒f'(t)=f'1,f'2,f'3hence…

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, −12t) (a) If R(0) = (-1,4,-5),…

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Q: Q4: Find the unit tangent and unit normal vector at t = 2 on the curve x = t? – 1, y = 4t – 3, z =…

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Q: sketch the curve represented by the vector-valued function and give the orientation of the curve.…

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Q: Find the second derivative of the vector-valued function 7(t) = (4t + 5 sin(t))i + (6t + 3 cos(t))j…

A: By using derivative of function

Q: Find the domain of the vector function (in interval notation) r(t)= t-1/t+1i+sin(t)j+ln(9-t^2)k

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Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

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Q: Find the domain of the vector-valued function r(t)=ln(t-1)i+Square root 4-tj

A: This vector valued function is a combination  of two functions: 1. Logarithmic function and 2.…

Q: Find the derivative of the vector function r(t) = In(5 – t²)i+/16 +tj+ 7e 8t k r'(t) = (

A: Given vector valued function is rt=ln5-t2i+16+tj+7e-8tk