multivariable calculus

1. [-/1 Points] DETAILS SCALCET9 13.1.002. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = cos(t) i + In(t) j + 1 - 3 -k Need Help? Read It Submit Answer 2. [-/1 Points] DETAILS SCALCET9 13.1.003.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find each of the following limits. lim e-2t t- 0 +2 lim t-0 sin (t) lim tan(4t) = t- 0 Find the limit of the given vector function. lim e -2ti+ . +2 -j + tan(4t) k t - 0 sin2(t) Need Help? Read ItMY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 3. [-/1 Points] DETAILS SCALCET9 13.1.008. Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t) = (+2 - 3, t) 4 2/ X X X - X -4 -2 2 4 -4 - 2 2 4 -4 -2 12 4 -4 -2 2 4 -2 -2 -2 -2 -4 -4 O Need Help? Read It5. [-/1 Points] DETAILS SCALCET9 13.1.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, 0, 0), Q(-5, 3, 6) vector equation r(t) = parametric equations ( x (t ) , y (t ) , z (t ) ) = Need Help? Read It Watch It 6. [-/1 Points] DETAILS SCALCET9 13.1.033. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the plane that contains the curve with the given vector equation. r(t) = (5 sin(t), cos(t), -cos(t)) Need Help? Read It7. [-/1 Points] DETAILS SCALCET9 13.1.034. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the plane that contains the curve with the given vector equation. r(t) = (5t, sin(t), t + 7) Need Help? Read It 8. [-/1 Points] DETAILS SCALCET9 13.1.039.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER At what points does the curve r(t) = ti + (4t - to) k intersect the paraboloid z = x2 + y?? (smaller t-value) (x, y, z) = (larger t-value) ( x, y, z) = Need Help? Read It Watch It Master It9. [-/1 Points] DETAILS SCALCET9 13.1.040. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER At what points does the helix r(t) = (sin(t), cos(t), t) intersect the sphere x2 + y2 + z? = 17? (Round your answers to three decimal places. If an answer does not exist, enter DNE.) smaller t-value ( x, y, Z ) = larger t-value ( x, y, Z ) = Need Help? Read It 10. [-/1 Points] DETAILS SCALCET9 13.1.052. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 3x2 + y2 and the parabolic cylinder y = 5x2 r(t) = Need Help? Read It