limit x^2 x-2/x^4-16
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Answer:
Explanation:
x
4
−
16
=
(
x
2
)
2
−
4
2
=
(
x
2
−
4
)
(
x
2
+
4
)
=
(
x
2
−
2
2
)
(
x
2
+
4
)
=
(
x
−
2
)
(
x
+
2
)
(
x
2
+
4
)
So:
x
4
−
16
x
−
2
=
(
x
−
2
)
(
x
+
2
)
(
x
2
+
4
)
(
x
−
2
)
=
(
x
+
2
)
(
x
2
+
4
)
with exclusion
x
≠
2
Hence:
lim
x
→
2
x
4
−
16
x
−
2
=
lim
x
→
2
(
(
x
+
2
)
(
x
2
+
4
)
)
=
(
(
2
)
+
2
)
(
(
2
)
2
+
4
)
=
4
⋅
8
=
32
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