Chapter 2
Determine exact limits using various limit rules.
Determine if a function is continuous or discontinuous at certain
points and be able to explain why.
Solve limit problems involving infinit
Name: _
Class Time:
_
MATH 151 Reading Assignment
2.1 Stewart
Answer the following questions after you read through the section briefly.
What does the word tangent mean in Latin?
What does the word s
intersection, how fast is the distance between the cars changing? Is the distance
increasing or decreasing?
Newtonville
>
Car
A
LCar
B
5) Find the absolute minimum and maximum values of y = x3 9x + 8
Sample Questions
1) Solve the following limit problems, using the method indicated:
. t2 9
a) ggm (use algebraic techniques, as in chapter 2)
1x+lnx
1. 9 ' 7 l h
b) xlnml + c 073 (use L Hospltal s RuL
Mathematica Quick Reference Sheet
Note: The purpose of this reference sheet is to give you quick reminders of the commands, shortcuts and general syntax rules that you learned in theSCCC Mathematica T
Lesson Plan 10/10
Warm-Up:
Identify the variables below as categorical or quantitative
.1. Number of cups of coffee consumed per day by SCC students
2. Type of coffee drink ordered at Starbucks
Secti
10/12 LP
WarmUp:
In Order to study whether lQ level is related to birth order, data were collected
from a sample of 540 students on their birth order (Oldest/in Between/Youngest)
and their score on an
MATH 163
Ch. 9.3
The Dot Product
Recall, scalar multiplication:
Example: Calculating the work done by a force.
In calc 2, you calculated the work done by a constant force
F in moving an object a dist
37. Which of the following functions f has a removable disconti-
nuity at a? If the discontinuity is removable, nd a function 9
that agrees with f for x 71' a and is continuous at a.
(a)f(x)=:_11, a
4144 Use the Intermediate Value Theorem to show that there is
a root of the given equation in the specied interval.
41.x4+x3=0, (1,2) 413/;=1x, (0,1)
43.e"=32x, (0,1) 44.5inx=x2-x, (1,2)
2
. . x +x
EXAMPLE 10 End 11m .
x-> 3 - x
SOLUTION We divide numerator and denominator by x (the highest power of x that
occurs in the denominator):
, x2+x , x+l
11m =11m =0
xnoBx x>on3
1
x
becaus
EXAMPLE 2 Find Iim 1n(tan2x).
x>0
SOLUTION We introduce a new variable, t = tanzx. Then t E: 0 and
t = tanzx > tan20 = 0 as x>0 because tan is a continuous function. So, by (3),
we have
1im1n(tan2x) =
EXAMPLE 6 A difference of functions that become large Compute lim (x/x2 + 1 x).
xbw
SOLUTION Because both wt:2 + 1 and x are large when x is large, its difcult to see what
happens to their difference,
m EXAMPLE? Evaluate lim eV".
x>O'
SOLUTION If we let I = l/x, we know from Example 4 that I > -00 as x > 0'. There-
fore, by (7),
1ime"=1ime=0 -
xO' :> -
Name: _
Class Time: 9:00_
MATH 151 Reading Assignment
3.3 Stewart
Answer the following questions after you read through the section briefly.
Fill in a trig expression in order to create a trig identi