lim x tends to infinity x^3/2x^2-1
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Answer
Dylan C. · mason m
Apr 21, 2015
When youre taking the
lim
x
→
∞
x
3
−
2
x
2
+
3
x
−
4
4
x
3
−
3
x
2
+
2
x
−
1
notice that the highest degree of x is the same in both the numerator and the denominator.
When this specific occasion is true of your f(x) (i.e.
x
3
...
e
t
c
.
4
x
3
...
e
t
c
.
) divide both the numerator and denomitator by the highest degree of x .
For our problem this is
x
3
lim
x
→
∞
x
3
x
3
−
2
x
2
x
3
+
3
x
x
3
−
4
x
3
4
x
3
x
3
−
3
x
2
x
3
+
2
x
x
3
−
1
x
3
simplifying we have
lim
x
→
∞
1
−
2
x
+
3
x
2
−
4
x
3
4
−
3
x
+
2
x
2
−
1
x
3
Knowing that the
lim
x
→
∞
1
x
=
0
all the terms other than the
1
4
cancel to 0
Therefore
lim
x
→
∞
x
3
−
2
x
2
+
3
x
−
4
4
x
3
−
3
x
2
+
2
x
−
1
=
1
4
hope it is useful for you and have a sweet day today and happy rose day
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