Arrange 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. (see picture)

1.h(x)

2.i(x)

3.m(x)

4.k(x)

5.g(x)

6.l(x)

7.j(x)

8.f(x)

Step-by-step explanation:

Given:

l(x)= lim x→∞ 5x^2-4/x^2+1

Dividing by highest power of x i.e. x^2

l(x)= lim x→∞ (5-4/x^2)/(1+1/x^2)

As per infinity property of 4/x^2 and 1/x^2 = 0

l(x)= 5/1

l(x)=5

i(x)= lim x→∞ x-1/|1-4x|

Dividing by highest power of x i.e. x

i(x)= lim x→∞ (1-1/x) / |1/x-4|

As per infinity property of 1/x and 1/x = 0

i(x)= -1/4

i(x)=-o.25

f(x)=lim x→∞ x^2-1000/x-5

Dividing by highest power of x i.e. x^2

f(x)= lim x→∞ (1-1000/x^2) / (1/x-5/x^2)

As per infinity property of 1000/x^2 and 1/x and 5/x^2 = 0

f(x)= 1/0

f(x)=∞

m(x)=lim x→∞ 4x^2-6/1-4x^2

Dividing by highest power of x i.e. x^2

m(x)= lim x→∞ (4-6/x^2) / (1/x^2-4)

As per infinity property of 6/x^2 and 1/x^2 = 0

m(x)= -4/4

m(x)= -1

g(x)=lim x→∞ |4x-1|/x-4

Dividing by highest power of x i.e. x

g(x)= lim x→∞ (|4-1/x|) / (1-4/x)

As per infinity property of 1/x and 4/x = 0

g(x)= 4/1

g(x)= 4

h(x)=lim x→∞ x^3-x^2+4/1-3x^3

Dividing by highest power of x i.e. x^3

h(x)= lim x→∞ (1-1/x+4/x^3)/(1/x^3-3)

As per infinity property of 1/x ,4/x^3 and 1/x^3 = 0

h(x)= -1/3

h(x)= -0.333

k(x)=lim x→∞ 5x+1000/x^2

Dividing by highest power of x i.e. x^2

k(x)= lim x→∞ (5/x+1000/x^2)/(1)

As per infinity property of 5/x ,1000/x^2 = 0

k(x)= 0/1

k(x)=0

j(x)=lim x→∞ x^2-1/|7x-1|

Dividing by highest power of x i.e. x^2

j(x)= lim x→∞ (1-1/x^2)/(|7/x-1/x^2|)

As per infinity property of 1/x^2 ,1/x^2 and 7/x = 0

j(x)= 1/0

j(x)=∞

functions in ascending order will be:

h(x)

i(x)

m(x)

k(x)

g(x)

l(x)

j(x)

f(x) !