Intriguing integrals: Part IIIssue 54
Euler's formula for ex
We want to prove the identity
You might think this argument has made somewhat cavalier use of limits. The following argument, adapted from [1, pg 272], is close to Euler's original. He was even more bold in his use of limits!
Thinking about near , and its gradient, we see that, for infinitely small
 C.H. Edwards, The Historical Development of the Calculus, Springer-Verlag, 1979.