F(x, y) = M (x, y)i+N(x, y)j is a conservative vector field with potential function f(x, y) Use this information for parts A through C. 11. A) If C is made up of the line segments from the point (0,0) to the point (4,1) and from (4,1 to the point (2,7) and from (2,7) to the point (0,0) then what can be said about M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line integrals. В) If C is a simply connected curve from the point (a,b) to the point (c, d) then what can be said about M(x, y) dx+ N(x, y) dy ? Explain using theorems or properties of line C integrals. If C is the parameterized curve r(t) = x1 (t)i+ yj(t)j, astsb and C2 is the parameterized curve r,(s) = x2(s)i+ y2(s)j, c

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.