1. [-/4 Points] DETAILS LARCALCET7 13.6.046. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. f ( x, y) = 9x2 + 42 C = 97, P(3, -2) (a) Find the gradient of the function at P. Vf ( 3 , - 2 ) = (b) Find a unit vector that is normal to the level curvef(x, y) = c at P. (c) Find the tangent line to the level curve f(x, y) = c at P. (d) Sketch the level curve, the unit normal vector, and the tangent line in the xy-plane. O O X -6 -4 -2 2 -6 -4 -2 -2 - 6 O O 4 4 X -6 -4 -2 2 -6 -4 -2 2. -2 -21 -4 - 4 Need Help? Read It 2. [-/4 Points] DETAILS LARCALCET7 13.5.016. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find aw/as and aw/at using the appropriate Chain Rule. Function Values w= ys - 7x2y s = -5, t = 10 x = es, y = et aw as aw at Evaluate each partial derivative at the given values of s and t. aw as aw at Need Help? Read It3. [-/2 Points] DETAILS LARCALCET7 13.5.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. w = xy2 + x2z + yz2, x = th, y = 8t, z=8 (a) Find dw/dt using the appropriate Chain Rule. dw dt (b) Find dw/dt by converting w to a function of t before differentiating. aw dt Need Help? Read It 4. [-/4 Points] DETAILS LARCALCET7 13.3.084. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 15xey - 12ye-* azz 2x2 azz ayax azz ay 2 azz axay Need Help? Read It 5. [-/1 Points ] DETAILS LARCALCET7 13.3.071. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find all values of x and y such that fx(x, y) = 0 and f (x, y) = 0 simultaneously. f ( x, y) = x2 + 3xy + y2 - 7x - 8y+42 ( x, y) = ( Need Help? Read It 6. [-/4 Points] DETAILS LARCALCET7 12.2.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find r'(t), r"(t), r'(t) . r"(t), and r'(t) x r"(t). r (t ) = 2+2i - 2tj + 2+3 k 2 (a) (b) r"(t) (c) r'(t) . r" (t) (d) r'(t) x r" (t) Need Help? Read It7. [-/3 Points] DETAILS LARCALCET7 12.3.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 9. a(t) = 6i + 7k v(0) = 7j, r(0) = 0 v(t) = r(t) = r(9) = Need Help? Read It 8. [-/1 Points] DETAILS LARCALCET7 11.5.045. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (4, 0, 4), and (-4, -1, 8). Need Help? Read It