Answer:
The arrangement of the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity is given below;
m(x), k(x), i(x), g(x), l(x)
Step-by-step explanation:
Since the limit of all the function as x tends to infinity is a non-infinite value, the limit converges.
We must understand that lim of a/x as x tends to infinity is equivalent to zero where a is any constant.
Let's take the function one after the other.
For l(x) = 5x²-4/x²+1
Dividing through by highest power of x i.e x²
lim x-> \infty 5x²-4/x²+1
lim x-> \infty 5x²/x²-4/x²/x²/x²+1/x²
lim x->∞ 5-4/x²/1+1/x²
=5-4/∞/{1+1/∞²}
= 5-0/1+0
= 5/1
= 5
Hence lim x-> \infty 5x²-4/x²+1 = 5
Find the remaining solution in the attachment below.