Worksheet for Section 1.3 The Concept of Limit
V63.0121: Calculus I Spring 2010
1. Use the graph of the function f to decide whether the value of the given quantity exists. If it does, nd it. If not, explain why. y 4 3 2
2
1
1
2
3
4
5
x
2
(i) f (2) (ii) l
Name: Midterm Exam Calculus I 2:00 - 3:15 pm, October 15, 2008
This examination booklet contains 6 problems on 7 sheets of paper including the front cover. Do all of your work in this booklet and show all your computations. This is a closed book exam. No
CALCULUS I Mid-Term Exam I 1. (20%) Let f (x) = 3x2 2x + 1.
Prof. E. Hameiri Fall, 2008
(a) Write an equation of the line going through the points (1, f (1) and (2, f (2). (b) Find a point on the graph of f where the tangent line to the graph has the same
SOLUTIONS TO MIDTERM I
V63.0121.001.2008F
1. (a) y = 7x 5.
3 (b) ( 2 , 19 ), y = 7x 4 23 . 4
2. (a) Graph. (b) This function is continuous on (, +) and is dieren) tiable on (, 1) (1, +) because limh0+ f (1+hhf (1) = 1 but ) limh0 f (1+hhf (1) = 1. (c) a =
Calculus I - Fall 2009
Midterm Exam, October 14, 2009 In the following problems you are required to show all your work and provide the necessary explanations everywhere to get full credit. 1. For each of the following, decide if the limit exists. If it do
Calculus I - Fall 2009
Midterm Exam, October 14, 2009 In the following problems you are required to show all your work and provide the necessary explanations everywhere to get full credit. 1. For each of the following, decide if the limit exists. If it do
Name:
ID#:
Midterm I
Math 1a Introduction to Calculus October 24, 2007
Please check your section: version 1.1.1, 2008-10-10 15:48 0.0 1.0 1.1 1.2 2.0 2.1 3.0 Rules: This is a two-hour exam. Calculators are not allowed. Unless otherwise stated, show all of
Solutions to Midterm I
version 1.1.3, 2008-10-14 14:47
Math 1a Introduction to Calculus October 24, 2007
1
1. (10 Points)
Math 1a
Solutions to Midterm I
October 24, 2007
1
(a) (2 points) Let f be a function and a a point in the domain of f . State the den
Worksheet for Section 1.5 Continuity
V63.0121, Calculus I Spring 2010
1. Which of the following functions are continuous? (i) The temperature of a pie as it is taken from the freezer to the oven to the table. (ii) The temperature at a specic moment along
Name:
ID#:
Midterm Examination
Math V63.0121, sections 11/12/13 Calculus I October 16, 2008
version TRA-1.2-dev, 2008-10-16 00:30
Rules: This is a 75-minute exam. Calculators are not allowed. Unless otherwise stated, show all of your work. Full credit may
Solutions to Midterm Examination
version TRA-1.3.1, 2008-10-24 14:21
Math V63.0121, sections 11/12/13 Calculus I October 16, 2008
1
y 3 2 1
Math V63.0121
Solutions to Midterm Examination
October 16, 2008
1
1. (16 Points) Consider the two functions graphed
Name:
ID#:
Midterm Examination
Math V63.0121, sections 4/5/6 Calculus I October 15, 2008
version MWA-1.1, 2008-10-15 10:10
Rules: This is a 75-minute exam. Calculators are not allowed. Unless otherwise stated, show all of your work. Full credit may not be
Solutions to Midterm Examination
version MWA-1.3.1, 2009-03-02 23:28
Math V63.0121, sections 4/5/6 Calculus I October 15, 2008
1
y 3 2 1
Math V63.0121
Solutions to Midterm Examination
October 15, 2008
1
1. (16 Points) Consider the two functions graphed be
Calculus I Midterm Exam
Exercise 1 Compute the following limits; they might be nite, innite, or not exist. x2 4x 1) limx0 2 x 3x 4 x2 1 2) limx+ 3 x + 3x + 4 x+12 2) limx3 x3 1 1 4) limx0 2 x x +x
1
Exercise 2 What are the (horizontal or vertical) asympto
Answer all 6 problems, each worth 4 points, and show all necessary steps on the blue book. Put a box around the nal answer.
1. Sketch a graph of a function f that satises the following ve conditions
x 1
lim f (x) = 3,
x4
lim f (x) = 3,
x4+
lim f (x) = 3,
Calculus 1
Fall semester 2008
Midterm exam
This is a closed texbook/notes exam. Use of calculators or other computing tools is not permitted. Please use blue books exam sheets as scrap paper, ask the instructor if you need more. All the blue books (togeth
Solution to V63.0121.020, Fall 2008 Midterm, Problem 1(c)
October 13, 2009
x2 + 4x 2x . We can do this more than one way: x
We are asked to nd limx
(a) Dividing the fraction into a sum of two fractions:
x
lim
x2 + 4x 2x = lim x x = lim
x
x2 + 4x 2x x
MIDTERM 10/08
CALCULUS I - FALL 2008
Each question worths 20 points. Good luck! Have fun!
(1) Take a look at the graph of this strange function f and answer the following questions (dont need to justify anything, just mark one of the options):
(a) The dom
Math 141 Calculus I Sample Syllabus
Spring 2012
Instructor:
Office:
Email:
Office Hours:
Phone:
Webpage:
Course Description: Standard first-semester course in single variable, differential calculus with
applications, especially for students of science, en