Can l'Hospital's Rule be Used to Solve exp(i*k-a)*x=0 for x=inf?

[teroenza]

Homework Statement

In a solutions manual I read exp(i*k-a)*x=0 when x= inf. I don't see how this happens.

Homework Equations

The Attempt at a Solution

Is there a procedure for dealing with this like l'Hospital's rule?
Like if I distribute the x for exp(i*k*x-a*x) then substitute inf, and get exp(inf-inf).

 

[Ray Vickson]

Homework Statement

In a solutions manual I read exp(i*k-a)*x=0 when x= inf. I don't see how this happens.

Homework Equations

The Attempt at a Solution

Is there a procedure for dealing with this like l'Hospital's rule?
Like if I distribute the x for exp(i*k*x-a*x) then substitute inf, and get exp(inf-inf).

Assuming throughout that k is real, the statement is true if a > 0, false if a ≤ 0. For the case a > 0 we just have "exponential damping" of the form exp(-a*x)*f(x), where f(x) = exp(i*k*x) remains bounded.

RGV

 

[teroenza]

Yes, I'm sorry. a is positive and real. As is k