Mathematics 126 -- Calculus for Social Sciences 2

Exam 1 -- Things to Know

September 21, 2001

General Information

As announced in the course syllabus, the first full-period exam of the semester will be given in class on Friday, September 28. There will be seven or eight questions (maybe grouped together) similar to problems from the problem sets so far. You may use a graphing calculator on this exam, but calculators like the TI 89 or 92 with symbolic manipulation are not allowed on this or any other exam.

If there is interest, we could schedule an evening review session Tuesday or Wednesday next week. We will discuss this in class on Friday, 9/21.

Material To Know

The exam will cover all the material we have studied since the start of the semester -- the derivative review from Chapters 1-5 of the text, plus sections 6.1 - 6.6 from Chapter 6. You should know the following topics.

• The material on derivatives that we reviewed in the first week. Know the statement of the limit definition of the derivative:
  f'(x) = lim_{h -> 0} (f(x+h) - f(x))/h
  and how to compute derivatives of functions built up by sums, products, quotients, and compositions from power functions, e^x, and ln(x).
• Antiderivatives by basic formulas like power rule, rule for exponentials, etc.
• Antiderivatives by substitution
• Applied problems where you need to compute an antiderivative and use it to answer another question (for instance, Section 6.1,/68, 69, Section 6.2/55, 57, etc.
• Definite integrals -- be prepared to do a Riemann sum calculation with a small number of subintervals (say n = 4,5), for a relatively simple function
• The Fundamental Theorem of Calculus -- know a precise statement of this. I will not ask for the full proof/justification we did in class, though.
• Applications of definite integrals to average values of functions, area between curves.

Good Review Problems

• Problems like 11-30 from the Review Problems for Chapter 5 (page 437)
• Problems like 6.1/29-58
• Problems like 6.2/1-31
• Problems like 6.1/68, 69; 6.2/55, 57; 6.4/47,
• Problems like 6.3/13-16
• Problems like 6.4/27 - 37; 6.5/7 - 33
• Problems like 6.6/1-8, 35-40