Chap
Problem
Source
Seq
1
Consider the function
()
2
6i
f
5
8i
f
5
tt
ft
tC
t
+<
=
−+
≤
.
a)
Find the value of the constant C that makes the function
( )
f
t
continuous on
,
−∞ ∞
.
b)
Graph the function
f
t
.
c)
Is the (resulting) continuous function
( )
f
t
differentiable at all points in the interval
t
−∞ < < ∞
?
Explain.
200105
1
1
Compute the following limits.
If the limit is infinite, indicate whether it is
+∞
or
−∞
a)
2
21
lim
5
x
x
x
→−∞
+
+
b)
2
12
lim
2
x
x
x
+
→
−
−
c)
2
2
1
1
lim
2
y
y
yy
→−
−
−−
d)
2
2
lim
2
x
x
x
x
→
−
−
200312
1
1
Let
2
2
1
1
1
1
11
1
1
1
x
x
x
fx
x
x
x
x
x
−∞ <
< −
+
+
=−
≤
≤
−
−
<<
+
∞
+
a)
List all the values of x for which
f
x
is not continuous.
Calculate the following limits.
If the limit is infinite, indicate whether it is
+∞
or
−∞
.
b)
1
lim
x
f
x
+
→
c)
1
lim
x
f
x
−
→
d)
1
lim
x
f
x
+
e)
1
lim
x
f
x
−
f)
lim
x
f
x
→+∞
g)
lim
x
f
x
→−∞
200405
1
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View Full DocumentChap
Problem
Source
Seq
1
Calculate the following limits.
If the limit is infinite, indicate whether it is
+∞
or
−∞
.
a)
4
4
lim
4
x
x
x
+
→
−
b)
2
4
16
lim
2
x
x
x
→
−
−
c)
2
2
3
69
lim
9
t
tt
t
→−
++
−
d)
2
2
lim
9
x
xx
x
→∞
−
e)
0
42
lim
t
t
t
→
+−
200412
1
1
Consider the function
()
3
41
2
2
3
fx
x
x
+<
=
≥
a)
Find
3
f
.
b)
Find
2
lim
x
f
x
−
→
c)
Is
f
continuous at
2
x
=
?
Explain.
d)
Is
f
differentiable at
2
x
=
?
Explain
200512
2
2
Use the definition of the derivative to find the derivative of
2
1
3
x
=
.
Then find an equation
for the tangent line to the graph of
f
at
1
x
=
.
200105
2
2
Use the definition of the derivative to find
( )
f
x
′
where
2
1
x
=
+
.
200112
1
2
a)
Use implicit differentiation to find the slope of the tangent line to the curve
4
3
yx
y
+
=
at
the point (4, 1).
b)
Find an equation of the tangent line to the curve
4
3
y
+
=
at the point (4, 1).
200112
2
2
At a certain factory, the daily output is
( )
600
QK
K
=
units, where K denotes the capital
investment measure in units of $1000.
The current capital investment is $900,000.
Use calculus
to
estimate
the effect that an additional capital investment of $800 will have on the daily output.
200205
1
2
A manufacturer’s cost in dollars is
3
492
400
6
q
Cq
q
=+
+
, where q tons of steel are produced.
The current level of production is 4 tons.
Use calculus to estimate the amount by which the
manufacturer should decrease production to reduce the cost by 100 dollars.
200305
1
2
Consider the curve defined by the equation
33
25
2
3
0
xy y
x
y
−
+−+
=
.
Find the equation of
the tangent line to the curve at the point
( ) ( )
,1
,
2
xy
=
.
200305
2
2
In order to maintain the output of a certain factory at a constant level, the number x of permanent
workers and the number y of temporary workers are related by the formula
( )
2/3
1/2
80
10,400
y
=
Currently, the factory employs 1,000 permanent workers and 400 temporary workers.
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 Fall '07
 Vorel
 Calculus, Derivative, Lake C, Lake Plentiful

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