©Zarestky
Math 151 Quiz 6 Version B
NAME:_____KEY___________________________________
1.
(3 pts) Find D15 cos (3x ) .
Establish a pattern:
D cos (3x ) = (!sin 3x ) "3
D 2 cos (3x ) = (!cos 3x ) "32
D 3 cos (3x ) = (sin 3x ) "33
D 4 cos (3x ) = (cos 3x ) "34
So, D15 cos (3x ) will look like D 3 cos (3x ) with a different power of 3.
D15 cos (3x ) = (sin 3x ) !315
2.
(2 pts) For the following parametric equations, find
x (t ) = 5t 7 !3t 2 + 2
y (t ) = t 3 !9t
dx
= 35t 6 !6t
dt
dy
= 3t 2 !9
dt
dy
dy
3t 2 !9
= dt =
so
dx dx 35t 6 !6t
dt
dy
.
dx
3/8/2010
©Zarestky
3.
Math 151 Quiz 6 Version B
3/8/2010
(5 pts) At noon, ship A leaves a port traveling South at 32 km/hr. At the same time, Ship B leaves the
same port traveling East at 24 km/hr. At what rate is the distance between the ships changing after
30 minutes? For full credit, include a sketch.
b
Given:
da
db
= 32 km/hr and
= 24 km/hr.
dt
dt
After 30 minutes, a = 16 km and b = 12 km so
c=
a 2 + b2 = 162 +122 = 20
Find
dc
by using the Pythagorean Theorem and Implicit Differentiation.
dt
A
a 2 + b2 = c 2
da
db
dc
2a + 2b = 2c
dt
dt
dt
Substitute in the known values and solve for
2 (16)(32) + 2 (12)(24) = 2 (20)
dc
.
dt
dc
dt
dc 1600
=
= 40 km/hr
dt
40
Bonus: (1 pt) Simplify
(n + 3)!
n!
.
(n + 3)! (n + 3)(n + 2)(n +1) n!
n!
=
n!
a
= ( n + 3)( n + 2)( n +1)
(It is not necessary to multiply out the three terms.)
c
B