1. One of the two vector fields listed below is conservative. The other one is not...
1. One of the two vector fields listed below is conservative. The other one is not conservative. (a) Determine which one of these fields is conservative. Label the conservative field F and and find a potential function f for it. Label the other field G and prove that G is NOT conservative. (b) Use the fundamental theorem of line integrals to compute SCF . dr, where C is the curve parameterized by (c) Compute Jc G-dr, where C is the...
Full answers please (a) Which of these two fields (if any) are conservative on R3? Give detailed reasoning (b) Find potential functions for the fields that are conservative. (c) Calculate the line integrals |F - dr and G dr where C is the arc of the 2 2 curve formed by the intersection of the plane z = 4 and the surface z =-+9 4 in the first octant, oriented anti-clockwise when view from above (a) Which of these two...
1. Let F-yi(xr +6g) j + 2z k and (a) Which of these two fields (if any) are conservative on R3? Give detailed (b) Find potential functions for the fields that are conservative (c) Calculate the line integrals F dr and G dr where C is the arc of the reasoning r2 4 curve formed by the intersection of the plane z = 4 and the surface--+92 in the first octant, oriented anti-clockwise when view from above. 1. Let F-yi(xr...
I know Graph 1 is not conservative and Graph 2 is conservative but how can we find vector function F for Graph 2? Because F is deliberately not given. Project 1. Fundamental theorem of line integrals amenta al theorem of line integrals: if F is a In our course we learned the conservative vector field with potential f and C is a curve connecting point A to b, then F dr f(B) f(A). Moreover it happens if and only if...
we need to determine if the vector field depicted in graph 1 and graph 2 are conservative by using the last 3 bullets points in the picture Project 1. Fundamental theorem of line integrals In our course we learned the fundamental theorem of line integrals: if F is a conservative vector field with potential f and C is a curve connecting point A to b, then f-dr = f(B)-f(A). Moreover it happens if and only if for any closed curve...
Let F-_y i + (z + 6y) j+2z k and 1. (a) Which of these two fields (if any) are conservative on R3? Give detailed reasoning. (b) Find potential functions for the fields that are conservative (c) Calculate the line integralsF dr and G dr where C is the arc of the curve formed by the intersection of the plane4 and the surface+ in the first octant, oriented anti-clockwise when view from above. Let F-_y i + (z + 6y)...
4. Use the Fundamental Theorem for Conservative Vector Fields to compute F. dr. where F= <3y2 - 4x3y3,6xy - 3x*y2 > and C is parametrized by r(t) = < e. +9 > from t = 0 to 1= 2.
8 points each 1. F is a conservative vector field. Evaluate ScF. dr where F =< 2xy3-4, 3x2y224, 4x^y323 > and C is the curve beginning at (3, 0, 5) and ending at (3, 2, -1)
is a conservative vector field (on its implied domain) a. Find its potential function b. Find where C is the curve shown below and given by the vector equation Solve using concepts of Vector Fields, Line Integrals, and/or The Fundamental Theorem for Line Integrals. +sec2 F dr (sin-t-2, cos-t-2, cos(nt) 式t) 3 2 2 1 2 1 0 2 +sec2 F dr (sin-t-2, cos-t-2, cos(nt) 式t) 3 2 2 1 2 1 0 2
G-ly~2 _ cos(x + y2z)ļi + [xz2-2yz cos(x + y2z)| j + 12.ryz-v2 cos(x + y%)| k. (a) Which of these two fields (if any) are conservative on R? Give detailed (b) Find potential functions for the fields that are conservative. (c) Calculate the line integralsF - dr and / G dr where C is the arc of the reasoning 2 2 curve formed by the intersection of the plane 4 and the surface zy in the first octant, oriented...