MthT 430 PreTest

In class August 29, 2007 - Turn in September 5, 2007

Group Work Rules:

·

You are encouraged to work together!

·

Away from the group, do your own neat write up of the problems.

·

Acknowledge the group members and any other person/source you use.

PreTest

The following problems include definitions and proofs which will be developed later in the course. Use your [group's] current understanding of functions , limits , continuous functions, derivatives , ¼, to try the following problems.

1.

lim_{h ® 0} [(e^h - 1)/h].

2.

lim_{x ® 0} [sin(x)/x].

3.

Express .232323¼ as a rational number. Hint: .232323¼ = 23[1/(10²)] + 23[1/(10⁴)] + 23[1/(10⁶)] + ¼.

4.

(True/False) There is a continuous function f₁(x), defined for all real numbers x, which takes on every value exactly once .

5.

(True/False) There is a continuous function f₂(x), defined for all real numbers x, which takes on every value exactly twice .

6.

(True/False) There is a continuous function f₃(x), defined for all real numbers x, which takes on every value exactly three times .

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On 20 Aug 2007, 07:50.