General Instructions (repeated, but with alterations):

• This midterm exam will consist of ten questions. Each of my TAs and I will grade either one or two questions on everyone's paper.We will try to make sure that most questions do not have multiple parts.
• 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 2 Content:

Midterm Exam 2 will cover those sections of Chapter 2 outlined on the class syllabus

Chapter 2

Sec 1:

• the material here is mainly conceptual in preparation for later sections
• be familiar with the idea of finding tangents by looking at secant lines connecting neighboring points on a graph
• be familiar with average velocity and how instantaneous velocity is the limit of average velocity over short time intervals

Sec 2:

• know the definition of the derivative of a function as a limit
• be able to compute the derivative directly from the definition for
  • simple polynomial
  • simple rational functions
  • simple square root functions
• know the statement and meaning of Theorem 2.1
• be able to draw graphs of the different ways in which a function fails to be differentiable at a point (see Figure 2.19a, b, c, d)

Sec 3:

• know the power rule and how to use it in simple example (review your rules for exponents in case you need to simplify an exponent of put an expression in exponent form before differentiating)
• know the content and ways to apply Theorem 3.3 on sums, difference, scalar multiples of functions
• be able to compute higher derivatives of simple functions
• be able to do simple velocity and acceleration problems

Sec 4:

• know the form of the product, reciprocal and quotient derivative rules
• be able to apply these rules efficiently in simple examples

Sec 5:

• know the Chain Rule for differentiating composite functions
• be able to apply this rule efficiently in simple examples
• know how the derivatives of f and f ^-1 are related

Sec 6:

• know by heart the formulas for the derivatives of the six primary trig functions (Theorems 6.1, 6.2, 6.3 and Table on page 200)
• be able to use these derivatives in more complex differentiations involving products, quotients, compositions, etc.

Sec 7:

• know the derivatives of e ^x, a ^x , ln x, log_a x
• be able to use these efficiently in more complex derivative calculations
• review Example 7.2 and be prepared for example calculations of this kind
• review Example 7.5 and be prepared for example calculations of this kind
• know the technique referred to as logarithmic differentiation and in particular how to differentiate functions of the form f(x) = x ^g(x), f(x) = h(x) ^x, and f(x) = h(x) ^g(x)

Sec 8:

• know what it means for a function to be defined implicitly (have a simple example such as x²+ y² = 4 in your head to illustrate)
• know the technique for finding derivatives of functions defined implicitly
• know the formulas for the derivatives of sin^-1x, cos^-1x, tan^-1x
• be able to use these formulas in complex derivative calculations

Sec 9:

• be able to give a precise statement of the Mean Value Theorem (Theorem9.4) and be able to illustrate what it says with a simple graphical argument
• review Example 9.3 and be prepared for an example calculation of this type