Q5: Plot the function y= 2 tan(t)-cos(mt) labeling the x and y axes. Where t is a vector containing the values within[1,10] with length 50

Q: Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t)…

A: Curve length problem..

Q: Find the domain of the vector-value function 7 (t) = (- 2 sin(t), – 5 cos(t), In(t – 1)) Domain: {t…

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Q: Represent the plane curve by a vector-valued function. r(t) =

A: Let's represent the plane curve by a vector valued function.

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: please help me with this exercise

A: Given,

Q: determine the unit vector from which f grows faster in P and determine a rate of change of f in P in…

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Q: /Find the tangent and normal vector for curve r= (5sin n i+5 cos n j+n k) n=(In 2t)

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Q: Find the unit vector in the direction in which f (x,y) =x+ sin(x + 2 ·y) increases most rapidly at…

A: Given: The given function is fx,y=x+sin(x+2y) at P(0,0).

Q: Find a unit vector in the direction in which f (x, y) = 8 cos(5x – 3y) decreases most rapidly at P…

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Q: Find a unit vector in the direction in which f(x,y, z) + %3D increases most rapidly at P(1, 2, -2),…

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Q: 5Let MH)=Hit2costj + (2shnt-3k a) Find unit tingent vector TH) of rtH)

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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: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

Q: Show that at every point on the curve r (t) = ⟨et cos t, et sin t, et⟩ the angle between the unit…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution is given below

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: This is a problem related to vector calculation. Based on the general formula we will find the…

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: Describe the curve represented by the vector-valued function r (t) = (2 cos t) i +tj + (2sin t) k…

A: Given: r→(t) =2costi→+tj→+2sintk→. x=2costy=tz=2sint Then, x2=costz2=sint

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: A particle moves in a path defined by vector-valued fanction FH)= (4)i +(zt-3)j + ( 3t - 3t) 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 tunction. (Entar your answer using interval notation.) r(t) = (V/25 -…

A: " Since you have asked multiple questions we will solve first question for you. If you need the…

Q: Consider the curve defined as r(t) = e^ti + e^tj + t k Determine the point on the curve where the…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t) , sin(3t) , sin( when…

A: Given r(t)=cos(t) , sin(3t) , sin(t) Compare it with r(t)=x(t) , y(t) , z(t) to obtain…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given: The cylinder x2 + y2 = 25 Surface z = xy

Q: Show that at every point on the curver(t) = ⟨et cos t, et sin t, et ⟩ the angle between the unit…

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Q: Find a normal vector at point P. xy2 - 4x2 + y + 8x = 7, P(4, 3) Find a tangent vector at point P.

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Q: Prove that the tangent vector is always orthogonal tothe position vector for the vector-valued…

A: Given r(t) =⟨sin t, sint cos t, cos2 t⟩.  we need to prove that the tangent vector is always…

Q: Consider an object moving according to the function from position r(t) = acoswt i + asenwt j. To…

A: As per the question we have to find the tangential and normal vector components of the path defined…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

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Q: The position vector of a moving particle in space at time t is given by the vector function r (t) =…

A: position vector of particle in space r→(t)=12(5-t)2i→+(2t-1)j→+43(5-t)32k→

Q: Q5) Let f(x, y) = Find unit vector for which Duf(2,3) = 0. %3D x+y

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve F(t)…

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Q: Sketch the curve represented by the vector-valued function                               r(t) = ⟨…

A: Given  r(t) = ⟨ cos t, sin t ⟩

Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

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Q: A particle moves on a fixed surface in F.(0), which is defined by z = 2xy. During the motion, the x…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(t), cos(3t), cos(t)) when…

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Q: Identify the direction from graph of functions given below: vector i) r = i(2 cos 21)+ j(2sin 2r) ;…

A: Given, r→=i^(2cos2t)+j^(2sin2t) Identify the direction vector, From the given position vector,…

Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x2 + y2 = = 81…

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Q: (a) Find the domain of the vector function r(t) and sketch its range, where r(t) = (v25 – t², 1, vf²…

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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: Find the binormal vector for 7(t) = (3t, sint, cos t) А. ВО cost, sint V10 10 1 B(e) = (- 3 В. ВО)…

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Q: The vector-function gives a particle velocity as function of time: T(t) =, and the particle position…

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Q: Consider the curve defined by r = ht, 2, ln(sec(t))i. Compute the (a) unit tangent, (b) unit normal,…

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Q: (a) f(r, y) = xª – x²y+y² +6 at P(-1,1) (b) f(r, y) = 2 sin(2x – 3y) at P(0, 7)

A: Please see the explanation below

Q: A particle moves in a path defined by vector-valuedl function. F4)= )i+(zt-3)j+ ( 3t - 3t)K, where…

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Q: Find the position vector for the particle with acceleration, initial velocity, and initial postion…

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Q: The temperature T, at a point (x, y) in the xy-plane is given by T(x, y) = 4x^2y^3 degrees Celsius.…

A: We have to find a unit vector in the direction in which the temperaturedecreases most rapidly at (2,…

Q: For the vector 3x+5y-1=0.what is the normal vector (n). find the direction for this vector.

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: First we find partial derivative with respect to x and y.