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Math Assignment: Function

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Added on  2020-05-28

Math Assignment: Function

   Added on 2020-05-28

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Running head: MATH ASSIGNMENT1Math AssignmentNameInstitution
Math Assignment: Function_1
Math ASSIGNMENT2Math AssignmentQuestion 1 For a conservative vector field, ∇f=⃗F where f is the potential function.Where, ∂f∂x=2x, ∂f∂y=2yey2+z,∧∂f∂z=ey2+z+coszf(x,y,z)=∫2xdx=x2+C1(y,z)f(x,y,z)=∫2yey2+zdy=ey2+z+C2(x,z)f(x,y,z)=∫(ey2+z+cosz)dz=ey2+z+sinz+C3(x,y)Therefore, the potential field f(x,y,z)=x2+ey2+z+sinz+CQuestion 2Part aIf we let L1,L2,L3¿L4 be the four sides of the rectangle then, L1 will be the line joining the points (0,0)∧(3,0), L2(3,0)∧(3,1), L3 points (3,1)∧(0,1), and L4(0,1)∧(0,0). We can parametrize Li as shown in table 1Table 1: Parametric formiXitXi'tF(Xi't)F(Xi't).Xi't1(3t,0)(3,0)(0,9t2)02(3,t)(0,1)(3t,9)93(3−3t,1)(-3,0)(3−3t,(3−3t)2)−3(3−3t)4(0,1−t)(0,-1)(0,0)0
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