Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an object at time t. Part a) Find a vector-valued function a(t) representing the object's acceleration at time t. Part b) What is the distance travelled by the object between time t = 0 and time t 1?

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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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: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

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Q: 1. Find the directional derivative of f(x,y) = In(a2 + y²) at the point P(2,1) in the direction of…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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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: What is special about the derivatives of vector functions of con-stant length? Give an example.

A: What is special about the derivatives of vector functions of constant length

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

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Q: determine the magnitude of the force exerted by block Y on block X during this acceleration.

A: In this question, we need to find the force exerted by block Y on block X.

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

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Q: 3:) Consider the function g defined by g(x ,y) = cos( mxVy) + log3 (x-y) (b) calculate the…

A: Given,g(x, y)=cosπxy+1log3(x-y)To find: Instantaneous rate of change of g(x, y) at point (4,1,2) in…

Q: Suppose that f (1,2) = 3 and that the directional derivative of f at point (1,2) in the direction of…

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: Example 4 Find the directional derivative off(x. y. z) = xy -v+at the point (1,-2,0) in the…

A: If f is differentiable at x,y,z  , then f has a directional derivative in the direction of any…

Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction…

A: Firstly, we calculate unit vector in direction of vector u.

Q: Find the tangential and normal components of acceleration for the positio denoted by ř = (cos 2t,–…

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Q: (True/False) Suppose the work done by a force F on a particle moving along a path C is given by x,…

A: True.

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

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point (1,3)…

Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a&gt;0 and it's constant here we have to see the effect of b so,…

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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

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Q: A projectile of mass m is launched from an initial position r0 with an initial velocity v0. Find its…

A: Consider the given initial velocity v0 and initial position r0

Q: Suppose that a motion described by the vector valued function (i.e. position function) r(t) has…

A: Given that :- r't=vt=5cost , 5sint ,-2 and r0=2,1,,1 find position function rt

Q: Find the derivative of f at the point P( – 3, – 2) in the direction of = ( – 1, – 1) | -(– 3, – 2) =…

A: Given, f(x,y)=-0.02x2y3   (b) The directional derivative for a function f(x,y) in the direction of…

Q: Find the directional derivative of the function f(, y) = In(x +y°) at the point (- 1,3) in the…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the directional derivative of function f(x y)=x°e' at the point (1,1) and direction of vector…

A: Given:       fx,y=x2ey    at the point 1,1 and direction of vector v=2i      fxx,y=∂∂xx2ey…

Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: Find First and second derivatives of Funchion . tm - (e-a -a)(e-a+a) Where a is parameber

A: To find a first and second derivative by first simplify the equation and finding it's value at x=0

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

A: Given Data:  Function: fx, y=sin6x+y Unit vector: u=cosθi+sinθj Point: Px, y=P0, π Angle: θ=-5π6

Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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Q: Choose the direction vector for which the function f defined by f(x, y)= sin(3x) cos(11y) has the…

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Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: What is special about the derivatives of vector functions of constant length? Give an example.

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: Find the directional derivative of the function f(r,y) In(z +y") at the point (2, direction of the…

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Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: Find the work done if a force of F-4i + 7j Newtons moves an object from point A(-9,0) to the point…

A: Here we have to find the work done. The solution is following.

Q: Find the directional derivative of the function f(x, y) = In(x² + y*) at the point (– 3, – 1) in the…

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Q: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

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

A: Solution

Q: 3. Find the directional derivative of the function f (x, y)= sin (xy) at a point -2i +j in the…

A: The given function: f(x, y)=sin2(xy)P=34, πu→=-2i^+j^5

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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