the directionat derivative of the fellowing Hawl Find g functions at foint Po in direction of the Vector A, fex 2 P(x24,2 = 3asyz Pologasa) A-2i+j-2k

Q: Q.2: Solve the higher differential equation below; yiv – y = 2 cos x

A: yiv-y=2cosx The above differential equation can be written as D4-1y=2cosx      , D=ddx The Auxiliary…

Q: determine directional derivative f(x, y) = x²y³ – 4y on point (-1,2) on vector direction v = (2, 1).…

A: The partial derivatives of f at (x,y)=(-1,2) are : ∂f∂x=2xy3   and   ∂f∂y=3y2x2-4. Therefore,…

Q: of f(x, y, tion of ve

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Q: flxy)=e* fleyl-e siny = é^ Find the directional derivofive in the direction of the vector that +60°…

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Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: 6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of…

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Q: i If (a,ß), a<0 is the unit vector that is parallel to the tangent line to the curve y=-1x²-x at the…

A: The equation of the given curve is            y = -x2 - x        =&gt; dy/dx = -2x - 1 So, slope of…

Q: What is the derivative of a function ƒ(x, y) at a point P0 in the direction of a unit vector u? What…

A: For a function z=f(x,y): the partial derivative with respect to x gives the rate of change of f in…

Q: What is the graph of r(t)=2 costi + sintj?

A: Vector-valued function : It is a function of the form  r(t)=f(t)i⏜+g(t)j⏜ or…

Q: C- Find unit vectors tangent and normal to the curves (y=4sine x-1-3cos8) at 8=:

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Q: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

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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: 2. Let 7(t) = (1, tv2, In(t)). (a) Find 7"(t). (b) Find 7(t) and simplify completely. (c) Find the…

A: Given, r→t=12t2, t2, lnt Used differentiation formulas, ddxxn=nxn-1ddxlnx=1xddxCfx=Cddxfx    C is…

Q: Part B please g(x,y,z)=x^2+y^2+(z-3)^2

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Q: Find the Derivative of a Vector-Value Function Given the vector-valued functions u(t)= et + e-5tj -…

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Q: Subtracting the two equations, find a vector equation for the curve of 3 intersection between y =…

A: Here, the two equations are y=4x2+34z2  and  y-1=3x2+12z2 for x&gt;0. We will be finding a vector…

Q: Consider the vector-valued function. (a) Show that is continuous at t = -1. (b) Evaluate (R. RY(2).…

A: Like a scalar function, features like continuity and differentiability are also demonstrated by…

Q: Find Components of the Acceleration For the curve defined by T(t) = (e-t cos(t), e' sin(t)) |3D find…

A: To find- For the curve defined by r→t = e-tcost, et sint, find the unit tangent vector, unit normal…

Q: 3. Find a particular solution up to u + 2xu, = y by first trying w = zy as the solution.

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Q: A point moving a long a curve whose position vector is R(t)=(t sin t +cost)i+(sin t-t cost)j+4 k;…

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Q: (a) What is the maximum directional derivative of g(x, y) = y²e2¤ at (2, – 1) and in the direction…

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Q: 2. [-/16.66 Points] DETAILS Find the directional derivative of the function at the given point in…

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