In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough detail in your wording that someone could easily sketch it.
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- Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.a)What is the slope of the tangent line to the curve y=2sin4x at x=⊼(pie)/4? b) Find a unit vector that is perpendicular to both u=(2,1,2) and v=(2,–2, –1) .2.b) Which vector is not normal at the plane defined by 2x - 4y-6z+1=0?
- Find a unit vector tangent to the curve of intersection of -x^2 - 2y^3 = z - 3 and 25/x2 - 4y - 3z^2 = - x + 6 at the point (1,1,0).give the position vectors of particles moving alongvarious curves in the xy-plane. In each case, find the particle’s velocityand acceleration vectors at the stated times, and sketch them asvectors on the curve. Motion on the parabola y = x2 + 1r(t) = ti + (t2 + 1)j; t = -1, 0, and 14 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.
- Prove that the vector T'(t) = 0 for moving in a straight line [hint: use r(s) = r0 + su]Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the point (π/2, π2/4).Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate f(-2.1, 3.1).