QUIZ #7: CALCULUS 1A (Stankova) Wednesday, March 10, 2004 Section 10:00–11:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Evaluate

lim_{x→e} \frac{e^{ln x} − e}{x − e}.

Explain your work.

Problem 2. Evaluate

lim_{x→0} \frac{sin((3 + x)^{2}) − sin 9}{x}.

Explain your work.

QUIZ #7: CALCULUS 1A (Stankova) Wednesday, March 10, 2004 Section 11:00–12:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Sketch the graph of f by hand and use your sketch to find the absolute (global) and local maximum and minimum values of f.

f(x) = \begin{cases}2x^{2} − 1, & if − 1 ≤ x < 0; \\ 1 − (x − 1)^{2}, & if 0 ≤ x ≤ 2. \end{cases}