G 726y Evaluate the limit, if it exists: lim (x,y)+(0,0) 28 + y4 7 7/2 0 Limit does not exist.
15. lim xy cos y (x, y)+(0,0) x2 + y4
j [3x2 +5y + i(x2-y2)] dz along (0,0) =x. |Evaluate
22. Tim (x,y) = (0,0) 2x² + 3y? x2 + +y? o 3 None of these 1 2
Question 12 1 pts Let f(x, y) = 2x – y + x2 + y4. Which (unit) direction vector u MINIMIZES the directional derivative Duf, at the point (0,0)? ANG 1 B)(- 2 V5 C) < tai D) (1, 2) OC B OA D
1. Compute the following limits. 9x4 - 4y4 (a) lim lim (x,y)–(0,0) 3x2 + 2y2
F(x, y) = (3x2 + sin y)i + (x cos y + 2 sin y)j. Question 1 (8 points) Find a potential function for the vector field F. Enter this function in the answer box. - Format B I U , . A X Question 2 (6 points) Use the potential function you found in problem 1 to evaluate F. dr, where Cis given by r(t) = (2-t)i + (ret/2), 0 st < 1.
Evaluate SSJ (+y– 32) 2V where E = {(x, y, z)| - 55y<0,0 < x <y, 0 <z<x+y?}
Evaluate the line integral of the function f(x,y)= (x+y2)/(sqrt(1+x2)) over the curve C: y=x^2/2 ; from (1,1/2) to (0,0)
Given the thermochemical equations X 2 + 3 Y 2⟶ 2 XY3 Δ H 1 = − 330 kJ X 2 + 2 Z2 ⟶ 2 XZ2 Δ H 2 = − 130 kJ 2 Y2 + Z2 ⟶ 2 Y2 Z Δ H 3 = − 250 kJ Calculate the change in enthalpy for the reaction. 4 XY3 + 7 Z2 ⟶ 6 Y2 Z + 4 XZ2 Δ H = kJ