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Unformatted text preview: Solutions to Quiz 2A
www.math.uﬂ.edu/ harringt
January 17, 2008
1
1. Let f (x) = x . Find f (x)−f (b)
.
x− b Be sure to SIMPLIFY.
−1
b
x−b
b−x
=
xb(x − b)
x−b
=−
xb(x − b)
1
=−
xb f (x) − f (b)
=
x−b 1
x 2. Find ALL values of x in the interval [0, 2π ] that satisfy sin x = tan x.
sin x
cos x
cos x sin x = sin x
cos x sin x − sin x = 0
sin x(cos x − 1) = 0
sin x = Thus, we have either sin x = 0 or cos x = 1.
(a) When sin x = 0, we have x = 0, π, 2π in our interval.
(b) When cos x = 1, we have x = 0, 2π in our interval.
Hence, our solution set is {0, π, 2π }. (Did you remember to check to
make sure we did not divide by zero?)
3. Determine the validity of the statement. 1 √
(a) ”The domain of x + 3 is (−3, ∞).”
√
This statement is FALSE. It should read ”The domain of x + 3
√
is [−3, ∞).” Notice that we allow −3 in the domain of x + 3.
(b) ”The graph of f (x + 2) is obtained by shifting f (x) two units to
the left.”
This statement is TRUE. 2 ...
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This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Math, Calculus, Geometry

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