©Zarestky
Math 151 Quiz 6 Version A
NAME:_____KEY___________________________________
1.
(3 pts) Find D18 cos (5x ) .
Establish a pattern:
D cos (5x ) = (!sin5x ) "5
D 2 cos (5x ) = (!cos5x ) "52
D 3 cos (5x ) = (sin5x ) "53
D 4 cos (5x ) = (cos5x ) "54
So, D18 cos (5x ) will look like D 2 cos (5x ) with a different power of 5.
D18 cos (5x ) = (!cos5x ) "518
2.
(2 pts) For the following parametric equations, find
x (t ) = 3t 6 ! 2t 4 +1
y (t ) = t 2 !6t
dx
= 18t 5 !8t 3
dt
dy
= 2t !6
dt
dy
dy
2t !6
= dt =
so
dx dx 18t 5 !8t 3
dt
dy
.
dx
3/8/2010
©Zarestky
3.
Math 151 Quiz 6 Version A
3/8/2010
(5 pts) At noon, ship A leaves a port traveling South at 40 km/hr. At the same time, Ship B leaves the
same port traveling East at 30 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
= 40 km/hr and
= 30 km/hr.
dt
dt
After 30 minutes, a = 20 km and b = 15 km so
c=
a 2 + b2 = 202 +152 = 25
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 (20)(40) + 2 (15)(30) = 2 (25)
dc
.
dt
dc
dt
dc 2500
=
= 50 km/hr
dt
50
Bonus: (1 pt) Simplify
(n + 4)!
n!
.
(n + 4)! (n + 4)(n + 3)(n + 2)(n +1) n!
n!
=
n!
a
= ( n + 4)( n + 3)( n + 2)( n +1)
(It is not necessary to multiply out the four terms.)
c
B