How Do You Solve Double Limits Involving Two Variables?

[utkarshakash]

Homework Statement

$\stackrel{lim}{y→0}\left( \stackrel{lim}{x→∞} \dfrac{\left( 1+\dfrac{ay}{x} \right)^x - \left( 1+\dfrac{by}{x} \right)^x}{y} \right)$

Homework Equations

The Attempt at a Solution

I need some hints. I really don't know how to solve these kinds of limits in which two variables are involved.

 

[dipole]

Just do the inner one first with y held constant, then do the outer one. If you know how to do one-dimensional limits then these are just as easy!

 

[HallsofIvy]

You need to know that $\lim_{x\to \infty}\left(1+ \frac{a}{x}\right)^x=e^a$