Nonuniform straight-line motion Consider the motion of an object given by the position function r ( t ) = f ( t ) 〈 a , b , c 〉 + 〈 x 0 , y 0 , z 0 〉 , for t ≥ 0 , where a, b, c , x 0 , y 0 , and z 0 are constants, and f is a differentiable scalar function, for t ≥ 0. a. Explain why this function describes motion along a line. b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?
Nonuniform straight-line motion Consider the motion of an object given by the position function r ( t ) = f ( t ) 〈 a , b , c 〉 + 〈 x 0 , y 0 , z 0 〉 , for t ≥ 0 , where a, b, c , x 0 , y 0 , and z 0 are constants, and f is a differentiable scalar function, for t ≥ 0. a. Explain why this function describes motion along a line. b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?
Solution Summary: The author explains why the function describes motion along a line.
Nonuniform straight-line motion Consider the motion of an object given by the position function r(t) = ƒ(t)⟨a, b, c⟩ + ⟨x0, y0, z0⟩, for t ≥ 0,where a, b, c, x0, y0, and z0 are constants, and ƒ is a differentiable scalar function, for t ≥ 0.a. Explain why r describes motion along a line.b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?
Calculus
Assume that the level surface equation x3+y3+z3+6xyz = 1 defines z implicitly as a function of x and y. Find zx(0, −1) and zy(0, −1). Use that information to find the equation of the plane tangent to the given level surface at the point corresponding to x = 0 and y = −1−1.
Using a Function (a) find the gradient of the function at P, (b) find a unit normal vector to the level curve f (x, y) = c at P, (c) find the tangent line to the level curve f (x, y) = c at P, and (d) sketch the level curve, the unit normal vector, and the tangent line in the xy-plane. f(x, y) = 9x2 + 4y2, c = 40, P(2, −1)
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