Step-by-step explanation:
Here we have
f
(
x
)
=
2
x
2
(
x
2
−
9
)
, which can be factorized as
f
(
x
)
=
2
x
2
(
x
+
3
)
(
x
−
3
)
As there is no common factor between numerator and denominator, there s no hole.
Further vertical asymptotes are
x
=
−
3
and
x
=
3
and as
f
(
x
)
=
2
x
2
(
x
2
−
9
)
=
2
1
−
9
x
2
, as
x
→
∞
,
f
(
x
)
→
2
, hence horizontal asymptote is
y
=
2
.
Observe that
f
(
−
x
)
=
f
(
x
)
and hence graph is symmetric w.r.t.
y
-axis. Further as
x
=
0
,
f
(
x
)
=
0
. Using calculas we can find that at
(
0
,
0
)
there is a local maxima as
d
y
d
x
=
−
36
x
(
x
2
−
9
)
2
and at
x
=
0
it is
0
. Further while for
x
<
−
3
and
x
>
3
, function is positive, for
−
3
<
x
<
3
function is negative.
Now take a few values of
x
say
{
−
10
,
−
7
,
−
4
,
−
2
,
−
1
,
1
,
2
,
4
,
7
,
10
}
and corresponding values of
f
(
x
)
are
{
2
18
91
,
2
9
20
,
4
4
7
,
−
1
3
5
,
−
1
4
,
−
1
4
,
−
1
3
5
,
4
4
7
,
2
9
20
,
2
18
91
}
Answer:
D.
Step-by-step explanation:
The cancels out to become x:
Split the
Put the cube root of y and cube root of 9 together:
By applying the Tan trigonometric formula, the value of the tangent for angle A is equal to: A. 3√91/91.
<h3>How to find the value of the tangent for <A?</h3>
In order to determine the value of the tangent for <A, we would apply Pythagorean theorem:
AB² = AC² + BC²
40² = AC² + 12²
AC² = 1600 - 144
AC = √1456
AC = 4√91 in.
Now, we can determine the value of the tangent for <A by applying the Tan trigonometric formula:
TanA = Opp/Adj
TanA = BC/AC
TanA = 12/4√91
TanA = 3√91/91.
Read more on trigonometry functions here: brainly.com/question/4515552
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