For each re, state which of the following strings is in the language of the re: ε, abba, bababb, and b.

a) (a+b)*ab(a+b)*

b) b* ab*ab*

c) a+(a*b)*

for each re, give two strings that are in ther corresponding language and two strings that are not:

a)a(a+b)*b

b)a*a+ε+b*

c) (ab+ba)*

For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.