Expii

# Change of Variables to Simplify Limits - Expii

Change of variables can help to simplify limits. The point is, if f is one-to-one (injective) on an open interval containing a, and the limit of f(x) as x->a is b and the limit of g(y) as y->b is c, then the limit of g(f(x)) as x->a is c. So if the limit of g(y) is hard to evaluate, you could try finding a good choice of (injective) f, plugging in y=f(x), and finding the limit of g(f(x)) instead -- this plugging in y=f(x) is the change of variables. While this may seem like a handful, it should help to see some examples of the idea in action.