L={^,b,bb,a,ab,abb,aa,aab,aabb,aaa,aaab,aaabb,aaaa,aaaab,aaabb}
x={^,b,bb} when y=ε
x={a,ab,abb} when y=a
x={aa,aab,aabb} when y=aa
x={aaa,aaab,aaabb} when y=aaa
x={aaaa,aaaab,aaabb} when y=aaaa
L1 contain length <=4 strings which present in L
answer is )L1={^,b,bb,a,ab,abb,aa,aab,aabb,aaa,aaab,aaaa}
Let L = {x|x = yz, y ∈ {a} ∗ ,z ∈ {Λ,b,bb}} Let L1 = {x|x ∈ L,|x| ≤ 4}. List all the strings in L1. List all the strings of the following language: L = {x|x ∈ {0,1} ∗ and |x| = 4 and x contains 01 as substring}
Sc 3x?yz ds, where C: x=t, y =ť, z = {1,0 <t<l.
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))
Prove that A = B for: A = {(x,y) e Rº : +y/<1} B = {(z,y) € RP: (71+ y)² < 1}
Let S be the surface of the box given by {(x, y, z) – 2 <<<0, -1<y<2, 0<z<3} with outward orientation. Let Ę =< -æln(yz), yln(yz), –22 > be a vector field in R3. Using the Divergence Theorem, compute the flux of F across S. That is, use the Divergence Theorem to compute SS F. ds S
(4) Let f(x) (0 if x<0 (a) Show that f is differentiable at z (b) Is f'continuous on R? Is f continuous on R? Justify your answer.
Let S be the surface of the box given by {(x, y, z)| – 2 < x < 0, -1 <y < 2, 0 Sz<3} with outward orientation. - Let F =< – xln(yz), yln(yz), –22 > be a vector field in R3. Using the Divergence Theorem, compute the flux of F across S. That is, use the Divergence Theorem to compute SSF. ds S
5. Let F(x, y, z) = (yz, xz, xy) and define 2 Crin = {(x,y,z) : x2 + y2 = r2, 2 = h} Show that for any r > 0 and h ER, le F. dx = 0 Crih
Evaluate SSS, (x² + y2 + z)ele?+y't??)? DV, where B is the unit ball: B={(x,y,z)/x² + y2 +2+ <1}
3. Let X and Y have a bivariate normal distribution with parameters x -3 , μΥ 10, σ 25, 9, and ρ 3/5. Compute (c) P(7<Y < 16). (d) P(7 < Y < 161X = 2).