2.4 One-Sided Limits
Definitions: (Side limits) Left-hand side limit; we write
This is the value that f(x) approaches, if it exists, when x approaches c
from the left, that is we consider values
Simil
Math 166 - Calculus II
Name:
Exam 1 - Practice
Section: (Circle one)
3
4
5
6
7
8
9
10
11
12
13
14
Instructions: This exam is closed book and closed notes. No sophisticated calculator is allowed. For f
SI Spring 18 Math 166 Chapter 6 Review
SI Leader:Eric Westfall
Teacher: Dagli
For the next 3 problems please use the following functions:
f(x)=(x)^()
g(x)= 3x/2-()
1. Using the Washer Method, set up b
Studying for Exam 1.
1. Know the definitions of Average Rate of Change, Limit, Continuous Function,
Continuous at a Point, and Instantaneous Rate of Change. You should be able
to write down these defi
Calculus I
8. The production costs, in dollars, per week of producing x widgets is given by,
56, 000
x
C(x) = 800+ 0.008x2 +
and the demand function for the widgets is given by,
p(x) = 350 0.05x 00l
Mathematics 165
Exam 1.9
Name:
September 16, 2017
Section:
Team:
Do not grade problem:
Read all directions carefully. Do any 4 of the 5 problems. You must indicate CLEARLY
the problem not to be counte
Mathematics 165
Exam 3.S
Name:
November 11, 2016
Section:
Do not grade problem:
Read all directions carefully. Do any 4 of the 5 problems. You must indicate
CLEARLY the problem not to be counted for c
Preparation for Exam 3
3.8 Inverse Functions
Understand and explain why a function f (x) must be one-to-one (that is must satisfy the
horizontal line test) if is to have an inverse, f 1 (x). Do not co
Practice Test 1 (MATH 165 Butler)
Student name:
This test is closed book and closed notes. No sophisticated calculator is allowed for this test. For full
credit show all of your work (legibly!). If yo
Practice Test 1 (MATH 165 Butler) Strident name:
This test is closed book and closed notes. No sophisticated calculator is allowed for this test. For full
credit show all of your work (legiblyl). If
Continuity Test
A function f(x) is continuous at an interior
point x=c of its domain if and only if:
1. f(x) is
2.
3.
We have three kinds of discontinuities:
Discontiniuty
Discontiniuty
Discontiniuty
2‘6 Limits lnvolvin
lottery
We are interested in the behavior of a function when the
magnitude of the independent variable x becomes
increasingly large, we write: X —+ 00 or X a _ co
plxl loge X <0
3.2 The Derivative as a Function
Last time we defined the derivative of y=f(x) at the point x: x0
¥\(2¢D= um $(x.+k)~ gm)
la
M-NJ
Definiﬁgn The derivative of the function f(x) with respect
to the vari
Name:
MATH 165 Section_ Exam 1 2/5/2016
SHOW ALL YOUR WORK to avoid loss of points.
tan(5;‘c)
1. Redeﬁne the function f(x) 2 ‘ so that it is continuous at x : 0., and hence for all real cc.
x
[H
3‘3 Differentiation Ruies
Derivative of a Constant Function f(x)=o
'( =t/i ’VXH‘B'RX): Linn C " C- :hwi O = O
4‘ X) [rm E k-VO k k—vd
”if m: (at; O ‘1
RQWGUUIG for positive integers: Let n be a po
Oblique Asymptotes (€26 maimed)
Let f(x) be a rational function, i.e.,
f<xr= :83)
If deg P(x) = deg S(x) +1 , then the graph of f(x) has an oblique
or slant line asymptote.
This means that, for la
Objective: To Solve Optimization Problems
Which is greatest? Which is least? Minimize, Maximize.
Used in Business for Cost, Production, Volume, Area
Environment for Volume, Area, Cost of Pollution
Ene
Calculus I
2
14. I1 et +3te5"2 dt
6 3
15f 84 27t dt
16.-[:/1+2y +(4y)(y2 8y+5)4 dy
17. J: e22 sin (e22 1) + sin (2) e2_s(z) dz
Applications of Integrals
Introduction
Here are a set of problems for