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Homework 2 Sample Questions - Calculus I | MATH 1210, Assignments of Calculus

Material Type: Assignment; Professor: Brown; Class: Calculus I; Subject: Mathematics; University: Southern Utah University; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 08/17/2009

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Math1210Chapter1Homework
Date LectureTopic AssignmentDue
Jan19 2.1
Jan22 2.2 1.6,2.1
Jan23 2.3
Jan24 HelpSession
Jan25 2.3 2.2,2.3PartI
Jan26 2.4
Jan29 2.5 2.3PartII,2.4
Jan30 2.6
Jan31 HelpSession
Feb1 Review 2.5,2.6
Feb2 Chapter2Exam ExtraCreditReview
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Math 1210 Chapter 1 Homework

Date Lecture Topic Assignment Due Jan 19 2. Jan 22 2.2 1.6,2. Jan 23 2.

Jan 24 Help Session Jan 25 2.3 2.2,2.3 Part I

Jan 26 2. Jan 29 2.5 2.3 Part II,2. Jan 30 2.

Jan 31 Help Session Feb 1 Review 2.5,2.

Feb 2 Chapter 2 Exam Extra Credit Review

A. In your own words, describe what a limit basically is.

B. How is f ( ) x L

x a

Æ

lim read?

C. What is a ones ided limit? Why is it useful?

D. True or False? f ( ) x

x

lim

Æ- 1

is the same as f ( ) x

x

lim

Æ 1 -

Quick Check Exercise pg 110 #

Exercises pg 110 112: 1, for #1 also find F ( ) x

x

lim

Æ 2

, 4,5,8,10,11,15a

E. True or False? It is possible for f ( a ) to be undefined and for f ( ) x

x a

lim

Æ

to exist anyway.

F. Find the following.

a. x x

lim

Æ 0 -

b. x x

lim

Æ 0 +

c. x x

lim

Æ 0 G. Find (^) x^1 0

lim^ sin

x Æ

. Try to reason it out before using a graphing calculator.

H. Do the following:

a. Graph ( )

x

x gx

b. Find g ( ) x

x

lim

Æ 2 -

c. Find g ( ) x

x

lim

Æ 2 +

d. Find g ( ) x

x

lim

Æ 2 e. Find g (2) I. What is a secant line? What is a tangent line?

J. Draw the tangent line to the graph shown at (1, 3 ). Draw the secant line through ( 2,0) and ( - 2 ,- 2 ).

pg 112: 17,21acd,

K. Fill in the blank. 0

is not defined. However, it is sometimes possible to get a number for 0

almost

almost ,

roughly speaking. For example, = Æ x

sinx x

lim

0

________.

Quick Check Exercises pg 152:1,2ab, pg 152 153: 1abcd,4abcd,5,9,10ab,11,13, A. What do limits have to do with continuity? B. On pg 144, three conditions required for f ( x ) to be continuous at a are listed. a. Give an example of a function that satisfies 1 & 2 but not 3. b. Give an example of a function that satisfies 2 but not 1. C. Give two examples of famous functions that are continuous. D. Give two examples of famous functions that are not continuous. E. What’s the difference between being continuous at a point and being continuous on an interval? F. Where are polynomials continuous? G. Where are rational functions continuous? H. The functions shown below are defined for all x except for one value of x. If possible, define f ( x ) at the exceptional point in a way that makes f ( x ) continuous for all x.

pg 153: 28,29b,30ab I. In your own words, explain what a removable discontinuity is. J. State the Intermediate Value Theorem (IVT) first exactly and then in your own words. Quick Check Exercises pg 152:4ab K. Prove the function f ( x ) = x^3 – 7 has an x intercept between 1 and 2. pg 154: 43 L. Why does the Intermediate Value Theorem (IVT) require that f is continuous?

Hw 2.6: Quick Check Exercises pg 159: 1abcdef,2ab(memorize part a!),3, pg 160 161: 1,4,6,7,17,19 24,26,28,29,30,31,35,39,41b,42b,49ac

A. Use the Squeezing Theorem to find (^) ˜ ¯

Á

Ë

Ê

Æ 3

2 0

lim x sin x x

pg 161 162: 69a,71,75a,78a