MULTIVARIABLE CALCULUS

1. [-/1 Points] DETAILS SCALCET9 13.2.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following vector equation. r (t ) = (+4, + 3 ) (a) Find r'(t). r' (t) = (b) Sketch the plane curve together with the position vector r(t) and the tangent vector r'(t) for the given value of t = 1. y 4 2 2 2 3 4 5 6 21 2 3 4 5 -2 -2 -4 -4 X O 10 -6 -4 -2 2 4 6 -4 -2 2 4 Need Help? Read It2. [-/1 Points] DETAILS SCALCET9 13.2.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following vector equation. r(t) = 3 sin(t)i - 2 cos(t)j (a) Find r'(t). r' (t ) = (b) Sketch the plane curve together with the position vector r(t) and the tangent vector r'(t) for the given value of t = Sit 4 4 X X -4 4 X -4 - 2 1 -4 -2 4 -4 4 - 2 -4 -4 -4 O - 6 Need Help? Read It3. [-/1 Points] DETAILS SCALCET9 13.2.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the derivative, r'(t), of the vector function. r(t) = tsi + cos(t ) j + sin2(t) k r' (t) = Need Help? Read It 4. [-/1 Points] DETAILS SCALCET9 13.2.017.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following vector function. r(t ) = (+2 - 4t, 1 + 5t, 1+3 + 1+2) Find each of the following. r'(t) = r'(5) = Ir'(5)1 = Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t ) = (+2 - 4t, 1 + 5t, 1+3 + 1+2 ), t= 5 T(5) = Need Help? Read It5. [-/1 Points] DETAILS SCALCET9 13.2.019.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following vector function. r(t) = cos(t) i + 8tj + 3 sin(2t) k Find each of the following. r'(t) = r'(0) = Ir'(0)1 = Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = cos(t) i + 8tj + 3 sin(2t)k, t = 0 T(0) = Need Help? Read It 6. [-/1 Points] DETAILS SCALCET9 13.2.024. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If r(t) = (e2t, e-6t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = T(0) = r"(0) = r'(0) x r"(0) = Need Help? Read It7. [-/1 Points] DETAILS SCALCET9 13.2.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 10 cos(t), y = 10 sin(t), z = 6 cos(2t), (5V3, 5, 3) (x (t), y(t), z(t) ) = Illustrate by graphing both the curve and the tangent line on a common screen. (The tangent line will be plotted for -1 s t s 1. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) Update Student Response Response Description Graph 20 Need Help? Read It9. [-/1 Points] DETAILS SCALCET9 13.2.035.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. r, (t) = (4t, t2, t4 ), "2(t) = (sin(t), sin(2t), 3t) Find r'] (t) and r'2(t). r'] (t ) = r'2 (t) = The curves r, (t) = (4t, t2, t*) and r2(t) = (sin(t), sin(2t), 3t) intersect at the origin. Find their angle of intersection, 0, correct to the nearest degree. 8 = Need Help? Read It 10. [-/1 Points] DETAILS SCALCET9 13.2.038. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral. 1 ( 913121 + (1 + 7 ) VEK ) at Need Help? Read It10. [-11 Points] SCALCET? 13.2333. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral. [4 (armi + (H nk) at 1 Need Help? 11. [-11 Points] SCALCETQ13.2.051. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find f'(3), where rm = \"(tj - um, \"(3) = (1, 2, 72), .113) = (5, a, a), and um = (t. {2, F). as: = |:l Need Help