x= infinite find root 9x2+2020 / x+7
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Step-by-step explanation:
Explanation:
We have the limit
lim
x
→
∞
√
9
x
+
x
2
x
4
+
7
Factor out the largest-degreed terms from the numerator and denominator of the fraction.
=
lim
x
→
∞
√
x
2
(
9
x
+
1
)
x
4
(
1
+
7
x
4
)
Note that the
√
x
2
can be brought from the square root as just
x
.
=
lim
x
→
∞
x
√
9
x
+
1
x
4
(
1
+
7
x
4
)
=
lim
x
→
∞
√
9
x
+
1
x
3
(
1
+
7
x
4
)
When analyzing this as it goes to infinity, we see that
- 9
x
and
7
x
4
go to
0
.
=
√
0
+
1
∞
(
0
+
1
)
=
1
∞
=
0
- There is also a more intuitive approach to limits of this type.
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