Many people first encounter the following limits in a Calculus textbook when trying to prove the derivative formulas for the sine function and the cosine function. These results aren’t immediately obvious and actually take a bit of work to justify. Any calculus text should provide more explanation if you’re interested in seeing it!
Special Limit Formulas in Calculus
By: Heather Hattori and Richard H. Langley and
Updated: 03-26-2016