Q1.

Consider the transcendental equation:

x + 1 + sech(x/

1. Seeking real solutions, explain why with no loss of generality.
2. After sketching the two functions in this equation on the same graph, explain why there is just one real-valued solution.
3. Find a two-term asymptotic approximation for this solution as .

Q2.

Consider the transcendental equation:

x tanx = 1, x >> 1.

1. What is an appropriate large parameter in this problem?
2. Find a three-term asymptotic approximation for x. What is the associated asymptotic sequence?

Q3.

Consider the eigenvalue problem we discussed in class:

(Ʌ +,

Where Ʌ is a diagonal N matrix with entries {. Find

 

= A + C2 22 = A + C2 22 = A + C2 22 = A + C2 22 = A + C2 22 = A + C2 22 = A + C2 22