Q1. Consider the transcendental equation: x + 1 + sech(x/ Seeking real solutions, explain why with no
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Q1.
Consider the transcendental equation:
x + 1 + sech(x/
- Seeking real solutions, explain why
with no loss of generality.
- After sketching the two functions in this equation on the same graph, explain why there is just one real-valued solution.
- Find a two-term asymptotic approximation for this solution as
.
Q2.
Consider the transcendental equation:
x tanx = 1, x >> 1.
- What is an appropriate large parameter in this problem?
- 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
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