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Q: Determine the domain of the vector function r() = cos(4t) i + 7in(t - 5) J - 10 Evaluate if the…

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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: Find the directional derivative of the function f(x, y) = xy at the point (x, y) = (-4,-6) in the…

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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: Find a vector G with curlG = sin xk.

A: Let F → = d1i+d2j+d3kThen curve F → =∇xF → =ijkddxddyddzf1f2f3Let us consider G→ = g1i+g2j+g3kThen…

Q: Derivatives of vector-valued functions Differentiate the following function.

A: We have given the function;

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: Solve the following differential equations (DEs) or initial values problems (IVPS): (b) 2xy x²+1 –…

A: The way of finding the value of constant 'C' is

Q: Find the directional derivative of the function f(x, y) = ln(x³ + y²) at the point (1, 3) in the…

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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: Find a unit vector that is tangent to the vector function F(t) = at t = 1. Step 1: take derivative…

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Q: For each problem, calculate the directional derivative in the given direction and the gradient…

A: z=x2-6y2  To Find: Directional derivative and gradient vector at P(7,2) in the direction of  a)…

Q: 7. Find the directional derivative of the function f(x, y, z)=(y+28) at (2, 1, 1) in the direction…

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

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…

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: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, -3, 5) and the direction in…

A: We will find the maximum rate of change and the direction.