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There are infinite limits, which are when the ends of a function go on to infinity and don't approach an asymptote. They have no maximum/minimum and can reach every point on the number line.

There also are indefinite integrals, which is the area between a curve and a line (say the x-axis), without a bounded region. These end in +C because the constant that may have been lost in the derivation process is unknown. If you have a point on the curve, you can find what C is, but in the neantime, an indefinite integral simply put is the area under a curve.

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Q: What are indefinite limits in calculus?
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What are the foundation of differential calculus and integral calculus?

The foundation, in both cases, is the concept of limits. Calculus may be said to be the "study of limits". You can apply a lot of calculus in practice without worrying too much about limits; but then we would be talking about practical applications, not about the foundation.


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What are the practical applications of limits of function?

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Basic calculus usually starts with limits. After that you continue with derivatives, and eventually you get to do integration.


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