Section 113 (Barsamian) Exam 1 Information

- Exam is on Friday, February 9, 2018.
- The exam starts after 2pm, as soon as all your stuff is put away
- The exam ends at 2:55pm, no exceptions
- You may need to draw straight lines, so bring a small ruler (or an ID or credit card).
- No calculators, no books, no notes, no cell phones.
**Note:**All exam problems are based on the list of suggested exercises from the textbook and class drills.- The Exam is 7 problems
- A problem involving
**Computing**.*y*-value and limits at particular*x*=*c*for a rational function*f*(*x*)- The problem will be of this form:
- Compute a
*y*-value at some particular*x*=*c*. - Compute limits at the same
*x*=*c*. - Using the results of parts
*a, b*explain what is happening on the graph of*f*(*x*) near*x*=*c*.

- Compute a
- The style of this problem will match the style of the problems on Quiz 2. Generally, scores were very low on Quiz 2. Giving you this much information about the exam problem almost amounts to a
*do-over*on Quiz 2. - To study for this problem
- Study Book Section 2.1 Examples # 8(A), 9 and their Matched Problems.
- Study Book Section 2.2 Examples # 1, 2 and their Matched Problems. (Notice that the book uses a different method than I use.)
- Lecture Notes from Day 2, 3, 4, 5
- Study Quiz 2 and the solutions that I provided for it.
- Study Reference 3 in the Course Packet
- Do Suggested Exercises 2.1 #61,79 (Remember: In Section 2.1, limits can only be numbers or DNE.)
- Do Suggested Exercises 2.2 #33, 35, 37, 39, 51, 53, 63, 64 (Remember: In Section 2.2, limits can be numbers, or infinity, or negative infinity, or DNE.)

- The problem will be of this form:
- A problem about
and**Limits at Infinity**for a rational function**Horizontal Asymptotes***f*(*x*). To study for this problem- Study Book Section 2.2 Example 5 and Matched Problem.
- Study Lecture Notes from Day 6
- Study Reference 4 in the Course Packet
- Do Suggested Exercises 2.2 # 43, 47, 51, 53, 63, 64, 65, 67, 69, 73, 89, 92

- A problem about
. To study for this problem**Continuity**- Study Book Section 2.3 Examples 1,2,3.
- Study Lecture Notes from Day 7
- Do Suggested Exercises 2.3 # 11,14,19,20,21,22,35,37

- A problem involving
.**Computing the Derivative of a Function Using Two Different Methods**- The problem will be of this form: Given the function
*f*(*x*).- Compute
*f '*(*x*) using the*Definition of the Derivative*. (That is, compute the limit involving*h*approaching 0.) Be sure to show all details clearly, and explain important steps, such as the step where you cancel*h/h*. - Start over: Compute
*f '*(*x*) using the*Basic Differentiation Properties*from Section 2.5.

- Compute
- Note that you should get the same results for parts (a),(b).
- The function
*f*(*x*) will be one of these three types:- Polynomial Function
- 1/
*x*type function - square-root type function

- To study for this problem
- For the Definition of the Derivative, study Book Section 2.4 Examples # 4,6,7 and their Matched Problems. (Notice that the book calls their method
*The Four Step Method*and they do not do a good job of explaining the important steps. I don't use The Four Step Method, and I explain the important steps thoroughly. You can use The Four Step Method, if you find it helpful, but you have to explain the important steps better than the book does.) - For the Basic Differentiation Properties, study Book Section 2.5 Examples 2A, 3AB, Matched Problem 3A, Example 4A, 5A and their Matched Problems
- Study Lecture Notes from Day 10, 11, 12, 13
- Study Reference 6 in the Course Packet for a list of the Basic Differentiation Properties/
- Do Suggested Exercises 2.4 # 19, 21, 27, 33, 35 (problems of the three types mentioned above) (Use the Definition of the Derivative.)
- Do those same five exercises again, but this time using Section 2.5 methods. (The Basic Differentiation Properties)

- For the Definition of the Derivative, study Book Section 2.4 Examples # 4,6,7 and their Matched Problems. (Notice that the book calls their method

- The problem will be of this form: Given the function
- (A problem like Class Drill 7) A problem involving
and**The Sum and Constant Multiple Rule****The Power Function**

The problem will be of this form: Given formula for*f*(*x*) involving sums of fractions that involve constants and powers of*x*,- Rewrite
*f*(*x*) as a sum of constants times power functions. (NO DERIVATIVES IN PART A!!) - Find
*f '*(*x*) using the derivative rules. Show all details clearly and use correct notation. Simplify your answer and rewrite it, if necessary, so that it does not contain any negative exponents.

- Study Book Section 2.5 Examples 4, 5 and their Matched Problems.
- Study Lecture Notes from Day 13, including Class Drill 7.
- Do Suggested exercises 2.5 # 19, 45, 51, 53, 55

- Rewrite
- A problem involving the
or the**Slope of a Tangent Line**(Using Section 2.5 Methods, The Basic Differentiation Properties.)**Equation of the Tangent Line**

To study for this problem,- Study Book Section 2.4 Example 5 and its Matched Problem (but use the Basic Differentiation Properties, rather than the Definition of the Derivative).
- Study Book Section 2.5 Examples 7,8 and their Matched Problems.
- Study Lecture Notes from Day 9 (but use the Basic Differentiation Properties, rather than the Definition of the Derivative) and Day 13.
- Do Suggested exercises 2.4 # 43D, 45C, 55AB (but use the Basic Differentiation Properties, rather than the Definition of the Derivative)
- Do Suggested exercises 2.5 # 59,63
- Study Class Drill 8

- A problem involving
**Marginal Quantities**

To study for this problem,- Study Book Section 2.7 Examples 1,2 and their Matched Problems.
- Study Lecture Notes from Day 14.
- Do Suggested exercises 2.7 # 1,2,3,9,13,17,33,43

- A problem involving

(page maintained by Mark Barsamian. Last Updated Feb 6, 2018)