What are the units of
f '
(
9
)?
(b) In general, will
f '
(
9
) be positive or negative?
pounds
pounds/dollar
pounds/(dollars/pound)
dollars
dollars/(pound/pound)
dollars/pound
positive
negative
Solution or Explanation
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6.
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Tafu is working with subatomic particles in the Physics lab. A positron is traveling in a straight line down
the particle accelerator. Tafu models its position with the function
p(t)=
t
2
t
– 1
where
t>1
. In the limit calculations below, if you need to use -
∞
or
∞
, enter -INFINITY or INFINITY.
(a) Calculate the limit
lim_(t->infty) p(t)
=
INFINITY
INFINITY
.
(b) Calculate the limit
pounds
pounds/dollar
pounds/(dollars/pound)
dollars
dollars/(pound/pound)
dollars/pound
positive
negative

2/21/14, 2:38 PM
Chapter 2.7 HW, Part 2
Page 7 of 11
.
(c) Calculate the limit
lim_(t->2) p(t)
=
(d) Let
a>1
be some fixed number. Let
h>0
be some small number. Write out a formula for the
slope of the secant line to the graph of
x=p(t)
between the point at
t=a
and the point at
t=a+h
(WARNING: When you write out an expression involving
a
and
h
, anytime you want to multiply
times
h
, you need to leave a single space between the two; i.e. "
a h
" means "
a
times
h
". In
contrast, if you write "
ah
" the computer=webassign thinks that you are talking about a new
variable called "
ah
". Alternatively, use the arithmetic buttons in the pop-up box whenever you
want to add, subtract, multiply or divide.):
(e) Keep
a
fixed and think of your formula in (d) as a function in the variable
h
. Call it
f(h)
Simplify your formula for
f(h)
as much as possible; your final answer should be a rational
function in
h
which is defined at
h=0
. (WARNING: When you write out an expression involving
and
h
, anytime you want to multiply
a
times
h
, you need to leave a single space between the
two; i.e. "
a h
" means "
a
times
h
". In contrast, if you write "
ah
" the computer=webassign thinks
that you are talking about a new variable called "
ah
". Alternatively, use the arithmetic buttons in
the pop-up box whenever you want to add, subtract, multiply or divide.):
(f) Calculate the limit
.
.
a
.
a

2/21/14, 2:38 PM
Chapter 2.7 HW, Part 2
Page 8 of 11