Given a regular language A, define L2 = { xz | there exists y
Σ*, xyz...
Given a regular language A, define L2 = { xz | there exists y
Σ*, xyz A, |x|=|z|, |y| = 2 }. Decide with a formal proof if L2 is
(a) regular; or (b) not regular but context-free; or (c) not
context-free.
The vector field given by E
(x,y,z) = (yz – 2x)
x + xz y + xy
z may represent an electrostatic field?
Why? If so, finding the potential F a from which E may be
obtained.
Define a Turing machine TM3 that decides language L3 = { w | w ∈
Σ*, #a(w) = #b(w) } over the alphabet Σ = {a,
b}.
IMPLEMENT USING JFLAP NO PAPER SOLUTION
Let L ⊆ Σ ∗ and define S(L), the suffix-language of L, as S(L) =
{w ∈ Σ ∗ | x = yw for some x ∈ L, y ∈ Σ ∗ } Show that if L is
regular, then S(L) is also regular.
The electrical voltage in a certain region of space is given by
the function V(x,y,z)=80+xz−sin(yz). If the directional derivative
of V at (1,1,π) in the direction 〈a,−1,π〉 is π, what is the value
of a?
Group of answer choices
π22
−π22
π2
−π2
None of the above.
Compute the derivative of the given vector field F. Evaluate the line integral of
F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.
Consider the scalar functions
f(x,y,z)g(x,y,z)=x^2+y^2+z^2,
g(x,y,z)=xy+xz+yz,
and=h(x,y,z)=√xyz
Which of the three vector fields ∇f∇f, ∇g∇g and ∇h∇h are
conservative?