), find
f
(
7
) and
f'
f
(
7
) =
f'
(
7
) =
(
7
).
.
1
7
1
7

a
(
t
)=
lim
t
→
pi
/2
−
a
(
t
)=
lim
t
→
0
+

2/21/14, 2:36 PM
Chapter 2.7 HW
Page 5 of 6
(d)
(e) With our restriction on
t
, the smallest
t
so that
a(t)=2
(f) With our restriction on
t
, the largest
t
so that
a(t)=2
(g) The average rate of change of the area of the triangle on the time interval [
π
/6,
π
/4] is
(g) The average rate of change of the area of the triangle on the time interval [
π
/4,
π
/3] is
(h) Create a table of values to study the average rate of change of the area of the triangle on the time intervals [
π
/6,
b
], as
approaches
π
/6 from the right. The limiting value is
(i) Create a table of values to study the average rate of change of the area of the triangle on the time intervals [
a
,
π
/3], as
approaches
π
/3 from the left. The limiting value is
a
(
t
)=
lim
→
pi
/4
is
is
.
.
b
.
a
.
t

2/21/14, 2:36 PM
Chapter 2.7 HW
Page 6 of 6
6.
12/12 points |
Previous Answers
The solutions
(x,y)
of the equation
x
2
+ 16
y
2
= 16 form an ellipse as pictured below. Consider the point
P
as pictured, with
x
-coordinate
(a) Let
h
be a small non-zero number and form the point
Q
with
x
-coordinate
1
+h
, as pictured. The slope of the secant line through
PQ
, denoted
s(h)
, is given by the formula
.
(b) Rationalize the numerator of your formula in (a) to rewrite the expression so that it looks like
f(h)/g(h)
, subject to these two
conditions: (1) the numerator
f(h)
defines a line of slope -1, (2) the function
f(h)/g(h)
is defined for
h=0
. When you do this
f(h)=
g(h)=
.
(c) The slope of the tangent line to the ellipse at the point
P
is
lim_(h->0) s(h)
=
1
.