# Differential Equations

Question1.Does the functionhave a vertical or horizontal asymptote? If so find the equation of the asymptote(s). If not, explicitly state that there are none.

2.Find

3.Find the derivative of

4.Find the derivative ofusing the definition of the derivative (DO NOT USE the rules of differentiation).

1.Find the antiderivative of

2.Find the antiderivative of

3.Find the area under the curve for the functionon the interval [1,2].

4.Your DNA code is composed of a series of four nucleotides: adenine, guanine, thymidine and cytosine (A, G, T and C, respectively).

1.What is the probability an individual has the following nucleotide sequence: “TATATA” at any particular position? You may assume independence.

2.What is the probability that an individual has k T’s in their DNA code at any particular position? (Note: k can be any integer and you may assume independence).

1.A local bank requires that customers must create a password in order to use their online banking services. The password must have a length of 8 and be composed of lower case letters and/or numbers (letters and numbers can be repeated).