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- Find the appropriate parametrization for the given piecewise smooth-curvein R^2, with the implied orientation. The curve C, which goes along the circle of radius 3, from the point(3,0) above the x-axis to the point (-3,0), and then in a straight line along the x-axis back to (3,0).Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).Determine the coefficient a, b ,c and d so that the cruve will satisfy the stipulated condition. Make the curve y=ax^3++bx^2+cx+d have the critical points at (1,0) and (-2,27)
- Obtain the dirfferential equation of the family of curves: 1. All circles passing through the origin and (0,4)Solve integral img1*when Γ is parametrically specified curve img2*const. a=7 ThanksConsider an q-curve with parameters 3 and 14. a. Determine q0.05. b. Find the q-value with area 0.01 to its right.
- Two curves are orthogonal if their tangent lines areperpendicular at each point of intersection. Show that the givenfamilies of curves are orthogonal trajectories of each other,that is, every curve in one family is orthogonal to every curvein the other family. Sketch both families of curves on the same axes. y = ax 3 , x 2+ 3 y 2 = b7.Find the maximum and minimum distances from (0,0) to the curve 5x2+6xy+5y2=8Find a parametrization for the curve described below. The line segment with endpoints (-2,4) and (0,5). X = ----- for 0 ≤ t ≤ 1
- find the frenet apparatus of curve 3u-u3 , 3u2 , 3u+u3 and Find equations of tangent, normal and binormal lines of this curve at the point 1 .Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameterHow do I find the bounds in which I integrate a curve that is rotated about an axis?