Question

May I know the examples of daily life that related to functions, limits, differentiation and integration? thank you

Come out with an equation for each topic and combine all the topics into one big application in your daily routine.

Answer 1

There's lots of examples you can make up, but just off the top of my head:

• How much to pay for electricity bills, etc. is an integral of your use at any time times the price of electricity at any time, i.e.
  `int " use"(t) * "price"(t) dt`

• If you want to find out how quickly your hair is growing, that's a derivative
  `(d)/(dt) "length of hair"= "hair growth rate"`

• If you want to figure out the maximum amount of money you can earn from investments, you need to find a limit. The classical one is compounding interest, which is something like

`lim_(n->infty) a_0 (1 + t/n)^n = a_0e^t`

• Functions can be implemented in a bunch of ways, but I guess the easiest non-trivial way would be to do something like travel time for an airplane. If you have to go across the United States and it takes 6 hours, you can figure out the average speed based on `d = rt`.