I wanted to find a postulate that was easier and faster than L’Hospital’s rule for solving limits because it is often extremely challenging to solve these limits with existing ideas. This is a postulate that succeeds in making it easier to solve these limits. I wanted to prove this postulate so that it could become a recognized part of Mathematics as we understand it. This can not only be useful to anyone who needs to deal with limits (think electricians with AC current) but also useful to those who will prove new concepts in Calculus with this postulate. I am using the restrictions of L’Hospital’s rule. This postulate should be used because it is easier and faster to use than L’Hospital’s rule and Trigonometric identities. It also lends itself to proving other arguments very well. It is also faster than existing methods and mathematically sound, as I will prove. This proof has explanations at each step.