Honors AP Calculus / Mr. Hansen	Name: _______________________________________
9/27/2006	Mr. Hansen’s use only (bonus point for spare batteries): _______

Straightforward Quest on §1-1 through §2-5

Please read: Calculator is OK throughout. Each problem is worth 7 points. Time limit: 35 minutes.

1.	State the formal definition of a limit at a point c. Be sure to use the phrase “if and only if” or the word “iff” in your definition.
2.	Write the correct notation for the definite integral of f (x) = –2x^2 + 7 from 0 to 3. Then make a sketch and estimate the integral by counting squares.
3.	If f (x) in #2 is a velocity function (feet per second) for a pastry truck, describe what your integral in #2 signifies. Be sure to include units and a description of what the answer means in context.
4, 5.	In #2 and #3, was there any moment in the interval [0, 3] at which the pastry truck was at rest? Find it and explain what the phrase “at rest” means in this problem.

6-8.	Use both the trapezoid rule and your calculator’s built-in quadrature function to estimate the integral of g(x) = 2^x + 3 from x = 1 to x = 3. Use 5 increments for the trapezoid rule. Show your work. Which answer is larger, and why?
9.	For the function , find the limit as x approaches 2. Justify each step with a word or two, and show every step.
10.	In #9, find the largest symmetric punctured interval of values of x for which f (x) is within 0.01 unit of the limit you found in #9. [No work need be shown, but use the letters d and e appropriately as you write up your answer. For this problem, please give at least 3 significant digits of accuracy, not the usual 3 decimal places.]