How are limits used in daily life? Please solve limit questions and relate them to daily life.

Hello!

You gave no specific questions, I think I should formulate them myself.

1. Alpha decay. Some types of atoms randomly emit alpha particles with the constant probability. For a large collection of such (identical) atoms a half of atoms will decay after some constant time, called half-life. After two half-life periods, 1/4 of the initial amount of atoms will remain, then 1/8 and so on.

So the number of initial atoms of that collection...

Hello!

You gave no specific questions, I think I should formulate them myself.

1. Alpha decay. Some types of atoms randomly emit alpha particles with the constant probability. For a large collection of such (identical) atoms a half of atoms will decay after some constant time, called half-life. After two half-life periods, 1/4 of the initial amount of atoms will remain, then 1/8 and so on.

So the number of initial atoms of that collection will decrease up to zero.

2. Atmosphere free falling. Any fixed object which falls in atmosphere asymptotically reaches its terminal velocity. This is an example of a finite nonzero limit in real life. The value of this limit depends on the horizontal surface area of an object and some other factors.

2.1. Warming. A frozen object pulled from a refrigerator slowly reaches the ambient temperature. In other words, the limit of an object's temperature is the ambient temperature.

3. (not from real life but a good limit:)
Imagine that we have a large pie and successive guests, and we give each next guest an of the remaining part of a pie. Then the part which remains to you will be Imagine that tends to infinity or simply is large (the total number of guests goes up and the one's part goes down correspondingly).

Then the remaining part will be about because

Here is the base of natural logarithms.

3.1. Compound interest.

occurs when we consider compound interest with the large compounding frequency ( is the nominal interest rate).