Student Name:
Sections 3.3 (Due: Thursday, 09/27)
Description
:
This homework will help you understand the formulas for the derivatives of the
standard trigonometric functions.
Show all work to get full credit.
1)
Differentiate the following functions.
f
(
x
) =
3
x
3

6 cos
x
2)
Find an equation of the tangent line to the curve
y
=
2
e
x
cos
x
at the given point
P
= (0,
2
).
3)
Find an equation of the tangent line to the curve
at the given point
P
= (0,
2
).
4)
Use the equations and relations given below to answer the following questions.
g
(
x
) =
f
(
x
)
sin
(
x
)
=
=
5)
Find the points on the curve below at which the tangent is horizontal. Use
n
as an arbitrary
integer. (Select all that apply.)
6)
A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation
of motion,
x
(
t
) where
t
is in seconds and
x
in centimeters, is given below.
x
(
t
) =
10 sin
(
t
)
(a) Find the velocity,
v
, and acceleration,
a
, at time
t
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Student Name:
v
(
t
) =
a
(
t
) =
(b) Find the position,
x
, velocity,
v
, and acceleration,
a
, of the mass at time
t
=
/
3
.
In what direction is it moving at that time?
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Noohi
 Calculus, Trigonometry, Derivative, Formulas, Acceleration, Velocity

Click to edit the document details