Class Meetingll4
Limits
gfFunctions
-Calculus
is
based
on tlis concept
-The
meaning of a
limit:
(informal)
As
x values
(independent
variablQ approaches
a fixed
value, then
the
y
values
,
{x)'s.
(dependent
variable}
get
closer
to
a
fixed value L.
(evel)
*Crraplicat
representatlon: -We
see &orn
the
graph
as
x values
converge
on a
(from
eitler side
of a), the
qx)
values
will
converge
on L.
(Eg.U
-Notatig!.
lim
{x)
=
tr
x-+a
-By
computing
f(x) at values for x near a
and observing
the
results,
one
can
guess
the
limit
L, ifthe
{x)
values seem to be
getting
closer to that
value.
-We
are only concernd
with x
values
near
4
not
at
)F4 so, there will be
a
limit
(sris0
even
ifthere is a
hole
in
the
graph
at
that
level.
Show
graphically.
(see
SS2)
*In
the
above
case, the
function
is
said
to
be
discontinuous
at
>r=a. This type
of
break
in
the
curve is
called
a
poipt
discontinuity.
A
good
way
to
think about continuity
is
to
think about
being
connectd.
Sw mywebsite.
-The
following
surve
does
not
have a limit as
x*>a
since
f(x) values approach different
values
as
x
approaches
a
tom
diferent sides. This curve
is discontinuous at:r=a.
This
type
of
break is called
a
iuunp
duequtiuulty.
(a
solid
dot means that there is
a
y
value
there
while an open dot
m€an$ there
isn't).
frsl
fi*
