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Calculus I                                                          Quiz #4                            February 24, 2004

Name____________________                   R.  Hammack                              Score ______
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(1)

(a)

(b)

(c)

(2)
Find the domain of the function

First, x can't be negative, for that would involve the square root of a negative number.
Second, x can't be such that 1+2cos(x) = 0, for that would result in division by zero.

The equation 1+2cos(x) = 0 reduces to cos(x) = -1/2,
so we are looking out for values of x that make cos(x) = -1/2.
Looking at the unit circle, you can see that and make cos(x) = -1/2.

Of course, you could add any multiple of to these values, and still cos(x) = -1/2,
making the denominator in f(x) zero.

Conclusion:  The domain is

(3)  In this problem, is a number between 0 and for which .

This information says ,
so it follows that  .  From this it follows that , so .
Then:
(a)
(b)