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Mathematics
Mathematics
Problem
Let
p
p
p
be the function
p
(
t
)
=
{
t
2
−
4
t
−
2
,
t
≠
2
,
L
,
t
=
2
,
p(t) = \begin{cases} \dfrac{t^{2}-4}{t-2}, & t \neq 2, \\ L, & t = 2, \end{cases}
p
(
t
)
=
⎩
⎨
⎧
t
−
2
t
2
−
4
,
L
,
t
=
2
,
t
=
2
,
where
L
L
L
is a constant. (a) Compute
lim
t
→
2
p
(
t
)
\displaystyle \lim_{t\to 2} p(t)
t
→
2
lim
p
(
t
)
. (b) Determine the value of
L
L
L
that makes
p
p
p
continuous at
t
=
2
t=2
t
=
2
, and verify your conclusion using the formal definition of continuity.
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