Remark:
1.
r'(
is
in
the
direction
of
the
tangent|line;
A
.
lf
=f{(©,
,
A(t)
ph
"t)
=f(),
g'(0),h’
2.
Hr()
(0,90,
hojpen
©
=H(O.9'O,h'O)
3.
r'(¢)
is
called
the
tangent
vector
to
the curve
as
long
as r’(t)
exists
and
The
curve
is|smoattl
it
continuous
and
r'(é)
Example
8:
Are
the
following
curves
smooth?
1.
r(t)
=chs(t),
t?e~',
cos*(t))
a
[cosce)]’
=
-
Sia(t)
feet]
=
-(e-ay(te®
)
[ws]
=
-2eat
ont.
F@
=
(-smo,
-e-nfe*,
-2estsine)
eS
——“——_
¥’@)=(0,
0,
0)
|X
————_—
~~
[tly]
Ar
NOT
smooth.
