Fall 2009 Math 151
3
Week in Review VI
Setion 3.7
1. Find the veloity and speed for the
urve
ourtesy: David J. Manuel
point
(overing 3.5, 3.6, 3.7)
r(t) = √
(4 sin t)i+(4 cos t)j at the
(2, −2 3).
2. Find a unit tangent vetor for the
r(t) = (t cos 2t)i + (t sin 2t)j
point where t = π .
urve
the
1
Setion 3.5
3. Given the position funtion of an ob-
r(t) = (4 cos t)i − (3 sin t)j, nd
r(0) and r′ (0) and use these to desribe
jet is
1. Find the derivatives of the following:
(a)
(b)
the motion of the objet.
f (x) = (x3 − 4)10
r1 (t) √= t2 i + t3 j and
r2 (t) =< 2 cos t, 2 sin t > interset at the point (1, 1). Find the angle
y = cos3 (2x)
4. The graphs of
√
(2x + 3)3
(4x2 − 1)8
()
f (x) =
(d)
y = (1 + x5 cot x)−8
of intersetion to the nearest degree.
2. Chain Rule Maplet*
*-Maplets loated at
http://allab.math.tamu.edu/maple/maplets/
f and g suh that
f (4) = 2, f (4) = −2, g(1) =
4, g ′(1) = 3, nd h′ (1) if h(x) =
f (g(x)).
3. Given funtions
′
2
(only works on OAL mahine, Callab mahine,
or any mahine with Maple installed on it)
Setion 3.6
1. Find
dy
dx
solve for
impliitly if
x2 y = 1.
y , dierentiate, and
Then
show you
get the same answer.
2. Find the slope of the line tangent to
sec(x + y) − tan(x − y) = 1 at the point
(π, π).
3. Impliit Dierentiation Maplet*
2
2
4. Show that the urves x + y
2
2
x + y = 2y are orthogonal.
5. The equations
mx
represent
at
x2 + y 2 = r 2
= 4x and
and
y =
families of urves
dierent onstants
r and m.
for
Show that
these families of urves are orthogonal.
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