DescriptionThe purpose of this thesis is to derive a variety of sophisticated limits, some in Mathematical Olympiad Problems, without using mathematically advanced concepts. In fact, this thesis requires only basic calculus and the Stolz-Ces`aro theorems. The latter will be presented without proofs but with all the necessary ingredients and formulas needed in this work. The thesis is written for a mathematically mature student with a certain level of preparation to tackle these beautiful limits.