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Mathematics
Mathematics
Problem
For
x
≠
2
,
3
x\ne2,3
x
=
2
,
3
let
k
(
x
)
=
(
x
−
2
)
(
x
+
1
)
(
x
−
2
)
(
x
−
3
)
,
k(x)=\frac{(x-2)(x+1)}{(x-2)(x-3)},
k
(
x
)
=
(
x
−
2
)
(
x
−
3
)
(
x
−
2
)
(
x
+
1
)
,
and define no value at
x
=
3
x=3
x
=
3
while setting
k
(
2
)
=
5
k(2)=5
k
(
2
)
=
5
. Determine the type of discontinuity of
k
k
k
at each specified point. Provide your answer in the form
x
=
2
x=2
x
=
2
: ____ ;
x
=
3
x=3
x
=
3
: ____ .
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