Chapter 1
Limits and Their Properties
f(x)=x3+2xl
f is continuous on [0, 1] with f (0) < 0 and
f(1) > 0.
Figure 1.37
EXAMPLE a An Application of the Intermediate Value Theorem
Use the Intermediate V
1.3 Evaluating Limits Analytically 67
l .3 Exam ISES See www.0alcChaicom ior workednut solutions tn odd-numbered exercises.
Exercises 14, use a graphing utility to graph the functi
54 Chapter 1 Limits and Their Properties
EXAMPLE El Using the 8-5 Definition of Limit
Use the 8-5 denition of limit to prove that
4+5 lim x2 : 4.
(2 + 02 x)2
4 Solution You must show that for each 8 >
104 Chapter 2 Differentiation
In Exercises 510, nd the slope of the tangent line to the graph 41. 3 42. y
of the function at the given point. 5 5
5. f(x) = 3 5):, (1,8) 6. g(x) = x +1, (2, 2) i 3
x 7.
104 chapter 2 Differentiatien
In Exercises 5 10, nd the slope of the tangent ne to the graph
of the function at the given point.
5.11;: 3 52:, (1.3) 6. gLr) = in: +1. (2, 2)
7'. gcfw_x = x2 - 9. (2. -
88 Chapter 1 Limits and Their Properties
3 EXEICISBS See www.83lcChatrom for worked-nut solutions to oddunumbered exercises.
In Exercises 14, determine whether f(x) app
146 Chapter 2 Differentiation
a EXB 31888 See wwwalcChatcom for worked-out solutions to oddnumbered exercises,
In Exercises 116, nd dy/dx by implicit differentiation. 31- Bifolium: 32- Folium of Desca
Review 3, MATH 136, ANSWERS
1.
a) f 1 ( x) 3 x 5 8
f (x)
f (x)
All real numbers or
All real numbers or
Domain
x 3/2 or
Range
y 9/2 or
3 3
, ,
2 2
9 9
, ,
2 2
x 9/2 or
y 3/2 or
9 9
, ,
2 2
Math 136 College Algebra
Review 3: Sections 4.1 4.5, 5.1 5.6
1. Find f 1 (x) for the following functions. State the domain and range for the function and
the inverse.
a) f ( x) ( x 8) 3 5
b) f (x)
9x
thmlmbnwm
no
The Taming of the Shrew Notes
Summary a! Scene (include the setting) 3 sentences minimum.
Most unpomnt quote from scene (Use original Shakespearean language):
Response (Le. "This quote
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you
What is Finite Math?
A very common question math faculty get is about the content of Math 124 Finite
Math. Unfortunately, no simple answer can be given in twenty-five words or less. But
that's why you