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Could someone explain how do we verify stokes theorem for the vector field F=zi + (2x+z)j + xk taken over the triangular surface S in the plane (x/1)+(y/2)+(z/3)=1 bounded by the planes x=0 y=0 and z=0. Take boundary of the above triangular surface as the path of the line integral.
For the surface integral I got,
integrate [x=0 - 1] , [y=0 , 2-2x] ( (1/14)*(54 - 38x - 27y) dx dy )
I got the y limit setting z=0 in the plane equation , ==> (y/2) + x = 1==> 2x+y=2 ==> y=2x-2 (Am i correct???)
When working it the other way around using curl, i got Curl F = -i + 2k
N = unt normal vector to the surface =k
N.k = 2/7
(Curl F). N = -2/7
Fnally got the integrate [(-2/7) ÷ (2/7) dx dy] , limits : [x=0 - 1] , [y=0 , 2-2x]
Finally I got -1 as the answer here.
Could someone point out my mistakes please?
How do we represent the above facts in 1)axiom form and 2)clausal form
1) All babies are innocent 2) Anyone who is innocent and affectionate will be loved by others 3) Anyone who is loved by others, will receive gifts 4) Teena is an affectionate baby
My thoughts on the question : (Let Vx and Ex denote universal and existential quantifiers respectively )
Let B(x) denote x is a baby I(x) denote x is innocent A(x) denote x is affectionate L(x) denote x is loved by others G(x) denote x receives a gift
Axiom Form : 1) Vx[ B(x) --> I(x) ] 2) Vx[ I(x) ^ A(x) ] --> L(x) 3) Vx [ L(x) --> G(x) ] 4) B(Teena) --> A(Teena)
Have I done the first part correctly? And how do we do the second part?
Given an array A of numbers of length n (indexed starting at 0), verify that the following pseu-docode program returns the index of the smallest element in the array. What is the LOOP invariant Hint: You should have more than one component to your loop invariant, and both minVal and minLoc should appear somewhere in the invariants. def findMin(A): n = length(A) minVal = A minLoc = 0 for (i = 1, i