1)For example, we wanna set up a rectangle field (instruct the length is x and the width is y ) with a stationary area S,then we can consider  the length(x) is an independent variable and the width(y) is the function of the length, giving the function:y=S/x(x>0).

In this case ,we can see the y approaches to 0 when x gets sufficiently large. So the horizontal asymptote of y=S/x is y=0

2)Think about a chocolate that is bisected many times,instruct the initial block of chocolate is 1,then the size of it becomes 1/2 after being bisected once ,and 1/4 after twice…

so, we can make a sequence for the remain size of the chocolate after being bisected n times:

(1/2)^n. We can notice that chocolate has the trend of decreasing when the times of bisecting increase. So the chocolate approaches 0 when n gets sufficiently large. (1/2)^n converges to 0

3)Think about n year after saving a sum of money in a bank(named as “a”) and the interest rate is “p”, then the first year we get interest ap , the second year we get total interest ap+ap(1+p),the third year…

so the nth year we get the total interest: ap+ap(1+p)+ap(1+p)^2+ap(1+p)^3…+ap(1+p)^n. it is worth of pointing out that it is a geometric series(the partial sum of sequence ap(1+p)^(n-1) ),because the common ratio of the sequence is (1+p)>1 so that series diverges