General Instructions:

• Each midterm exam will consist of six questions, usually multiple part. Each of my TAs and I will grade one question on everyone's paper.
• While I will not rule out the occasional multiple choice question, generally speaking all questions will be free response requiring you to show all your work. The logical steps getting you to an answer are worth much more than the final answer itself
• Your objective on an exam is to demonstrate that you understand the concepts and can carry out essential calculations. Therefore, you should add enough detail to your answers to convince the grader that you understand what you are doing.
• Studying and practicing homework problems is important for and exam, but not all questions on an exam are drawn from the homework. Questions can also be based upon examples I or my TAs have covered in lectures and discussions.
• Theory is also important. You could be asked to state simple definitions, describe concepts, or even state and prove simple theorems. This is all part of learning what Calculus is all about.

Calculator Use Instructions:

• Calculators are permitted (TI 84 or lower) on exams.
• THE STORAGE OF NOTES OR FORMULAS IN YOUR CALCULATOR IS PROHIBITED!
• Exam proctors are allowed to examine your calculator at any time before, during, or after the exam. The presence of notes or formulas in your calculator will be treated as a violation of academic integrity (cheating)
• If you borrow a calculator from a friend, YOU are responsible for making sure that it does not contain stored notes and/or formulas

MidTerm Exam 1 Content:

Midterm Exam 1 will cover those sections of Chapters 0 and 1 outlined on the class syllabus

Chapter 0

Sec 1:

• be prepared to solve elementary inequalities and state the solutions in interval form
• be able to find the equations of lines in the plane in various forms
• what is the vertical line test and how does it guarantee that a graph defines a function?
• what are the domain and range of a function and how do you find them?
• what is a polynomial? What is a rational function?
• be able to finds the zeros of a polynomial by factoring

Sec 3:

• know the definition of an inverse function. What does one-to-one mean?
• what is the horizontal line test and how does it guarantee the existence of an inverse
• know how to compute an inverse function in simple cases
• be familiar with the two facts: domain of f ^-1 = range of f and range of f ^-1 = domain of f
• know how the graphs of f and f ^-1 are related

Sec 4:

• be able to sketch quickly graphs of sin, cos, tan and know the definitions of sec, csc, cot
• be able to find the amplitude, period and frequency of a trig function
• know the definitions and graphs of sin ^-1, cos ^-1, and tan ^-1, including their domains and ranges
• know how to compute inverse trig function values using the "standard" triangles
• review Example 4.10 and know the technique

Sec 5:

• review the rules for exponent manipulation
• know the graphs of e ^x, e ^-x, b ^x , b ^-x
• know definition 5.2 of the logarithm and how the log and exponential (as inverse functions) cancel each other
• review the rules for manipulating logs
• be able to solve simple equations involving exponentials and logs

Sec 6:

• know the definition of a composite function and how to find the domain of such a function
• know how the graphs of f(x) + c, f(x + c), cf(x), and f(cx) are related to the graph of f(x)

Chapter 1

Sec 1:

• review for the general concept of a limit as visualized through slopes of tangents and arc length approximations

Sec 2:

• know the conceptual definition of right and left handed limits of a function f(x) at a point x = a
• know the definition of the derivative interms of one sided limits
• know several ways in which limits are undefined (i.e typical graphs)
• be familiar with an example involving a straight line with a hole in it

Sec 3:

• be able to state Theorem 3.1 on the rules for manipulating limits
• know how to evaluate the limits of polynomials
• know how to compute subtle limits that require prior cancellation of common factors
• know how to compute subtle limits involving the prior rationalizing of root
• review Theorem 3.4 for computing limits of exponential, log, trig and inverse trig functions
• what is the squeeze rule and why does it work (from a graphical perspective)?
• be able to apply the squeeze rule in simple cases

Sec 4:

• know the definition of continuity
• have three or four graphical example in your head of how a function can be discontinuous at a point
• what is a removeable discontinuity?
• know what standard functions are continuous: polynomials, rational functions where denominator does not vanish, roots, sin, cos, tan (where defined), etc.
• be able to determine where a function is continuous using Theorem 4.2's limit properties and know continuous functions

Sec 5:

• know what is meant by a vertical asymptote of a function and how to express this in terms of left/right handed limits being infinity or -infinity
• be able to find vertical asymptotes for simple functions
• know what is meant by an horizontal asymptote of a function and how to express this in terms of limits of the function as x approaches infinity or -infinity
• be able to find horizontal asymptotes for simple functions