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- 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).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) .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.
- Find unit vector tangent and normals to the are y=1/2 X3+1/2. Point(1,1)Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?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).
- What is the vector equation of the line tangent to the curve traced at x=1? Determine the curvature traced at x=1.What is the length of the acceleration vector of a particle travelingaround a circle of radius 2 cm with constant velocity 4 cm/s?Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (4, 16).
- What is the definition of the directional derivative for afunction of two variables, f (x, y)? Be sure to include thewords “unit vector” in your definition.Find a unit vector pointing in the direction in which the maximum rate of change occurs for the following function at the given point. f(x,y)=2xsin^2(xy)at the point (2,1). Express your answer as a unit vector and round the value(s) to three decimals.