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Mathematics
Mathematics
Problem
For a non-zero constant
a
a
a
, define
H
(
x
)
=
x
4
−
2
a
2
x
2
+
a
4
x
−
a
H(x)=\dfrac{x^{4}-2a^{2}x^{2}+a^{4}}{x-a}
H
(
x
)
=
x
−
a
x
4
−
2
a
2
x
2
+
a
4
. Assume
x
≠
a
x\neq a
x
=
a
. a. Part 1: Determine
lim
x
→
a
H
(
x
)
\displaystyle \lim_{x\to a} H(x)
x
→
a
lim
H
(
x
)
in terms of
a
a
a
, fully justifying each algebraic step.
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