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I would say that the fundamental idea to understand is the concept of changing ratios. Limits seems to me to be more a tool in order to calculate the ratios th

I would say that the fundamental idea to understand is the concept of changing ratios. Limits seems to me to be more a tool in order to calculate the ratios than a fundamental concept.

mclehman 9y ago
I agree with that. You can hand limits as a tool to someone already comfortable with the concepts and present them as a way to quantify their intuitive understanding.
- mannykannot 9y ago
  But without limits, you cannot actually do much with the concepts. Whether you call limits a concept or a tool, they are essential to the practice of calculus, and, historically, to its emergence (and not trivially so, either.)
  - throwawayjava 9y ago
    Yeah but you can do well on the AP calculus exam without understanding limits, if you can calculate derivatives and solve some word problems related to derivatives. Hence, the gap between "5 year old calculus" and "high school calculus" is smaller than the gap between "high school calculus" and "actual calculus"
    - deleted 9y ago
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