MULTIVARIABLE CALCULUS

1. [-/1 Points] DETAILS SCALCET9 13.3.003.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 s t 0 Find k'(x). K'(X) = At what point does the curve have maximum curvature? (x, y ) =( What happens to the curvature as x - co? k(x) approaches as x -+ co. Need Help? Read It10. [-/1 Points] DETAILS SCALCET9 13.3.051. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the vectors T, N, and B at the given point. r(t) = (+2, 2+3, t). (4, 10, 2) T N B = Need Help? Read It Watch It11. [-/1 Points] DETAILS SCALCET9 13.3.053.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following curve. x = sin(4t), y = -cos(4t), z = 16t Using the given parametric equations, give the corresponding vector equation r(t). r(t) = Find r'(t) and [r'(t)I. r' (t ) = Ir' (t) 1 = Find the equation of the normal plane of the given curve at the point (0, 1, 47). Now consider the osculating plane of the given curve at the point (0, 1, 47). Determine each of the following. T(t) = T'(t) = IT'(t) 1 = N(t) = Find the equation of the osculating plane of the given curve at the point (0, 1, 4n). Need Help? Read It12. [-/1 Points] DETAILS SCALCET9 13.3.055. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find equations of the osculating circles of the ellipse 25x2 + 4y = 100 at the points (2, 0) and (0, 5). at (2, 0) at (0, 5) Use a graphing calculator or computer to graph the ellipse and both osculating circles on the same screen. 15 15 y 25 X 10- 10 -15 -10 10 15 20 -5/ 15 -10 X X -25 -20 -15 -10 5 10 15 20 25 10 -15 -20 10- -10 JX -15 -10 10 15 -25 -15 [ 10 -15 Need Help? Read It Watch It13. [-/1 Points] DETAILS SCALCET9 13.3.057. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER At what point on the curve x = to, y = 6t, z = t* is the normal plane parallel to the plane 6x + 12y - 8z = 3? ( x, y, z) = Need Help? Read It Watch It 14. [-/1 Points] DETAILS SCALCET9 13.3.066. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the formula r(t) = - _ B'(t) . N() to find the torsion at the given value of t. |r'(t) r(t) = (sin(t), 5t, cos(t)), t= Need Help? Read It