16.3 Homework - The Fundamental Theorem (Homework)

1. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.3.002. A table of values of a function f with continuous gradient is given. y 0 1 2 X 0 4 8 1 1 3 5 7 2 6 2 9 Find Vf . dr, where C has the following parametric equations. c x=t+1, y=t'+t, Osts1 15 X Need Help? Read It2. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.3.004. M Determine whether or not F is a conservative vector field. If it is, find a function fsuch that F = Vf. (If the vector field is not conservative, enter DNE.) F(x, y) = (12 - 4x)i + 2xyj f ( x, y ) = x2 + 7v2 - 2xy - gy + k X Need Help? Read It3. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.3.007. Determine whether or not F is a conservative vector field. If it is, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE.) F(x, y) = (ye* + sin(y))i+ (e* + x cos(y))j f(x, y) = e sin (y) X Need Help? Read It Watch It4. [-/1 Points] DETAILS SCALCET9 16.3.009. MY NO Determine whether or not F is a conservative vector field. If it is, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE.) F(x, y) = (y cos(x) + cos(y)) i + (9y sin(x) - x sin(y))j f ( x, y ) = Need Help? Read It6. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.3.018. Consider F and C below. F(x, y) = (9 + 2xy )i + 2x yj, C is the arc of the hyperbola y = - _ from (1, 1) to ( 3, 1 X (a) Find a function f such that F = Vf. f( x, y ) = Ve. tz X (b) Use part (a) to evaluate F . dr along the given curve C. 15 X Need Help? Read It