Convergence of Saddle-Point Approximation for Large M in Integrals

[jfitz]

Can the method of steepest descent (saddle point method) be used if an integral has the following form:

$$\int exp\left[M f(x) + g(x)\right]dx$$

where M goes to infinity?

I ask because all the examples I've seen of this method involve a function which is multiplied by a very large number, but never with only part of the function getting big.

 

[jfitz]

Nevermind, I figured it out.