Show that the graph of the vector-valued function r(t) =< sin t, 2 cos t, /3 sin t > is a circle, and find its radius and center.

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: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(8t), sec(3t), r'(t) =

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Q: Find the derivative, r'(t), of the vector function. r(t) = tan(8t), sec(4t),

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Q: Given the vector-valued function r(t) =

A: Given  r→(t)=cost,3t,2sint

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: Represent the plane curve by a vector-valued function. x- + y2 = 4 r(t) = 2 cos ti +2 sin tj

A: x2 + y2 = 4 x2 + y2 = 22 = r2 Therefore, r = 2

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

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Q: Consider the vector-valued function 7(t) = (4sin(t), 7 cos(t)). Compute the following derivative…

A: r'(t) = &lt; 4cost, - 7sint&gt;

Q: Sketch the curve represented by the vector-valued function                               r(t) = 2…

A: Given information: Vector-valued function rt=2costi+tj+2sintk trigonometric identity, sin2t+cos2t=1…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A: For the solution follow the next steps.

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Givenf(x,y)=xx2+y2 , (2,1) , v=&lt;3,5&gt;

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: -2 -1

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Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction…

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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: Compute the directional derivative of the following function at the given point P in the direction…

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Q: Find the equation of the tangent line of the vector function F(t) = (e= cos(t), e=' sin(t), e') at…

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

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

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given :fx,y=sin8x+yp0, π

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: In this first we calculate derivative of g function then get a unit vector in the direction of v. So…

Q: Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at…

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Q: Find the derivative, r'(t), of the vector function. r(t) = a + 6tb + r'(t) = %3D

A: r(t) = a+6tb+t8cr'(t) = ddta+6tb+t8cr'(t) =dadt+ddt(6tb) +ddt(t8c)

Q: Find the second derivative of the vector-valued function F(t) = (5t + 4 sin(t))² + (2t + 4 cos(t))…

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Q: Find the second derivative of the vector-valued function F(t) = (4t + 6 sin(t))i + (3t + 2 cos(t))…

A: The answer is

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: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: The largest value of the constant b such that the vector-valued function F(t) =< cos 21It, sin (t-…

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Q: Find a vector equation of the line tangent to the graph of r(f) at the point Po on the curve. r(1) =…

A: Find the derivative of the function r(t) to find the equation tangent to the graph of the function.…

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

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Q: Given function f(x, y) = xy² - x² + 5y. a) Find the maximum rate of change of f at the point (1, -2)…

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Q: Find the derivative, r'(t), of the vector function. r(t) at cos(2t)i + b sin5(t)j + c cos³ (t)k…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

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 derivative, r'(t), of the vector function. r(t) = at cos(5t)i + b sin3(t)j + c cos5(t)k

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

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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: 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: If asked to find the directional derivative of f(r, y) in the direction of a NON unit vector (a…

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Q: Match the vector-valued function with its graph. O r(u, v) = 2 cos(v) cos(u)i + 2 cos(v) sin(u)j + 2…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

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Q: For the function f(x,y)=(4−x^2−y^2)/−5, find a unit tangent vector to the level curve at the point…

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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: The unit tangent vector of the function ⟨2t+1,(3t+1)^2,(2t+1)^3⟩ at the point with parameter value…

A: Topic - vectors Option d

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.