QUIZ #2: CALCULUS 1A (Stankova) Wednesday, February 4, 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 the limit, if it exists:

lim_{h→0} \frac{(3 + h)^{−1} − 3^{−1}}{h} .

QUIZ #2: CALCULUS 1A (Stankova) Wednesday, February 4, 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. Use the given graph of f to find a number δ such that

|f(x) − 3| < 0.3 whenever 0 < |x − 4| < δ.

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Problem 2. Prove the statement using the ϵ, δ definition of limit. Illustrate with a graph.

lim_{x→a} c = c.

[Hint: There may be more than one correct answer. Justify your reasoning.]