5 QUESTIONS, THEY ARE NOT MISSING DATA, GRAPH OR ANYTHING, PLEASE DOUBLE CHECK WORK, ILL UPVOTE YOUR WORK

1. 

Find the direction in which the maximum rate of change occurs for the function x, y) = 2a: Si{a:y) at the point (4,1). Give your answer as a unit vector. Use the gradient to find the tangent to a level curve For the function x, 3;) = 4:52 l 433; + 5y2 l 5:1: 5y 2, find a unit tangent vector to the level curve at the point ( 4, 1) that has a positive a: component. Round your numbers to four decimal places. For the function f(::, y) = ( 5 2:2 ya}, find a unit tangent vector to the level curve at the point ( 4, 5) that has a positive a: component. [a Calculate directional derivatives and gradients in three dimensions. Find an equation for the tangent plane to the surface 2 + 4 = my2 (206(2) at the point (4, l, D). [% Calculate Du3, 2, 4) in the direction of E = 2; 3 + 2; for the function 11333312) = $23$y+y2+3$+5y222+4mz. Round your answer to four decimal places