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How to express limits in terms of e? Limits at infinity | Exponential limits

In this video, I'll teach you how to express limits in terms of e? or you can say finding exponential limits. In an exponential function, a variable occurs in the power. We can also say finding or evaluating limits at infinity.

We cannot express limits in terms of e without a limit formula i.e. limit n approaches to infinity (1+1/n)^n which equals to e. I didn't prove the formula in this lecture but there are 4 conditions for this limit to be e which are as follows:

1) The first term should be +1
2) There should be a + sign in the middle
3) Reciprocal of 2nd term should be the power
4) On the direct limit, we should have indeterminant form 1 raised to the power infinity.

If the first term is not +1, we can form it. if there is no + sign in the middle, we can also make it. If we do not get power while taking reciprocal of 2nd term, we can also resolve this issue. But the 4th one is the most important condition. If we do not get indeterminant form 1 raised to the power infinity, we cannot make it possible. In this lecture and in the coming ones we will be learning how to form the first three conditions.

Once all the four conditions hold, we can put our limit as e. e is a constant between 2 and 3 and roundabout its value is 2.718281...

In this way, we can find exponential limits or limits at infinity in terms of e. That's all for today. Hope it helps.

Enjoy learning at my playlist calculus: Evaluating limits at
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