What is the value of this expression when n approaches infinity?
4−(4/n)+(5/n)+(15/3n^2)
A) 20
B) 10
C) 5
D) 4
E) 1
Use you "sense" of numbers to see what happens to the fractions as n gets larger.
(I think your last term should read 15/(3n^2) or else it becomes large as n gets large)
e.g. look at 5/n
suppose n = 100,000, then 5/n = .00005 , which is close to zero
suppose n = 1,000,000,000 , then 5/n = .000000005, even closer to zero
so as n gets really big
4/n and 5/n each ---> 0
and 15/(3n^2) ---> even faster
so you are stuck with
4 - 0 + 0 + 0 = 4
To find the value of the expression when n approaches infinity, we can use the concept of limits in calculus.
First, let's simplify the expression:
4 - (4/n) + (5/n) + (15/3n^2)
To evaluate this expression as n approaches infinity, we need to determine how the different terms behave as n gets larger and larger.
The term (4/n) approaches 0 as n becomes infinitely large. This is because dividing any number by infinity results in an infinitely small value, which is effectively 0.
The term (5/n) also approaches 0 as n approaches infinity for the same reason as mentioned above.
The term (15/3n^2) can be simplified to (5/n^2). As n gets larger and larger, the denominator n^2 increases faster than the numerator 5. Thus, the term (15/3n^2) approaches 0.
Therefore, the expression simplifies to:
4 + 0 + 0
Which equals 4.
So, the value of the expression when n approaches infinity is D) 4.