Asymptotic expansion CHALLENGE

[haywood]

Asymptotic expansion CHALLENGE!

KUDOS TO ANYONE WHO GETS THIS!

Homework Statement

For Perturbation Methods class we are supposed to find two-term asymptotic expansions for the two real roots of xe^-x = $$\epsilon$$as $$\epsilon$$-->0+

Homework Equations

xe^-x = $$\epsilon$$as $$\epsilon$$-->0+

x = $$\epsilon$$e^-x

The Attempt at a Solution

Graph x = $$\epsilon$$e^-x and y=x. Find the first root near 0; how do I find the second root and then the two-term asymptotic expansion for these two real roots??

 

[lippyka]

Answer: The two roots are approximately x_1 = 0 and x_2 = 2. The two-term asymptotic expansion for these two real roots is x_1 \approx 0 and x_2 \approx 2 - \frac{\epsilon}{2}.