Given the vector: j(x) sin(2x) X = X ,ex, 1-√1+x (2, 1,-2), x = 0 Determine its domain and show it is continuous at X=0. =), x = 0

Q: If/Given that → F(t)=(5t+3,3t²,8-4t³), Find: - a) The first derivative: b) The first derivative: c)…

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Q: Let h(x, y) be a differentiable function and let (xo, yo) be a point in the domain of h. Also, let u…

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Q: For what values of t is the vector-valued function, 7(t) = , continuous? | Domain: {t| <t< }

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Q: Suppose that f: R² → R² is a function such that f (1, 2) = the linear approximation. (Use syntax…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 sec me t…

A: We know position vector of bee if it has a velocity vector  is We are given

Q: R(t) = = {{In(3 In(3 – t), (0, -1, 4), 4t-8 4-t2⁹ 8), 3t² – 8 t#2 t = 2.

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Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: Given the vector-valued function r (t) = e-t i +t j +(tan t) k Find: a) r'(t) b) r"(t) c) r'(t) .…

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Q: Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an…

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Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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Q: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,

Q: consider the vector-valued function r(t) = a) State the domain of r(t) b) Identify where r(t) is…

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

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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: Given the vector-valued function

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Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

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