3. Find the equations of tangent and normal lines to the given curves at the given...
#1 Find the slope and the equations of the tangent lines to the given curves at each of the given points. 1. x= 2 cos e y = 3 sin TT a. r = 4 7T b. 2 2. x = cos 20 y = sin 40 TT a. r = 4 TC 2 b. r=
Q-1: a) find the equations of the tangent and normal to the curve x + 3xy + y = 5 at point (1,1). draw the equation of the ellipse b) Describe and 9x? + 4y +36x - 8y +4 = 0. (20marks)
Write equations of a tangent and a normal plane for the given curves at the given points: 9.8.1 is the question number. 9.8.1.x-t - sint, y- cos t, z-4sint/2 at t-/2; 9.8.1.x-t - sint, y- cos t, z-4sint/2 at t-/2;
Mathematic please i need a help Bo Find equations of the vertical lines that meet the curves (a) y = x + 2x - 4x+5 and (b) 34= 2 x + 9x -3x-3 in points at which the tangent lines to the two curves are parallel. tion: @ y = x + 27 - 4x + 5
2. Find tangent line, tangent vector and normal line, normal vector for each curves at the intersection point of the curves y = –2°, y = yx. Show calculation steps clear and cleanly.
Find equations for the tangent plane and the normal line at point P P. (Xo. No: 2) (5,1,0) on the surface - Cos (2x) + 6x2y+3e* + 2y2= 154. The equation for the tangent plane is a
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
48. Connecting Graphs and Equations The curves on the graph below are the graphs of the three curves given by 4x+ 5 = + 2x - x +3 y3= x3 - 2125x2 15 10 5 T T -21 -5-4 34 5 1 -5 -10 (a) Write an equation that can be solved to find the points of intersection of the graphs of yi and y2. (b) Write an equation that can be solved to find the x-intercepts of the graph...
Find an equation of the tangent plane and parametric equations of the normal line to the surface ?? − ?? 3 + ?? 2 = 2 at the point ?(−1, −1, 2).
12 marks] 8. Find the equations of both the tangent lines to the hyperbola x? - 4y2 = 9 that pass through the point (-3,3). Note that the point (-3, 3) is not on the hyperbola.