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Unit 3, Activity 4, The Local and Global Behavior of Ln x with Answers
Blackline Masters, Advanced MathPreCalculus
Page 93
Comprehensive Curriculum, Revised 2008
Part I
1. Graph the function
f
(
x
) = ln
x
.
Use a window with 1
≤
x
≤
10 and 10
≤
y
≤
5. Sketch
the graph. What is the domain of
f
(
x
)? For what values of
x
is
x
ln
< 0?
x
ln
= 0?
x
ln
>
0?
Run the trace feature and find the farthest point to the left on the graph.
What is it?
The domain is {x: x>0}.
lnx = 0 at x = 1 so lnx < 0 when x < 1 and lnx > 0 when x > 1.
The farthest point to the left is (.053, 2.93)
2. Reset your window to 0
≤
x
≤
0.01 and 10
≤
y
≤
6.
Sketch this graph. Run the trace
feature and find the farthest point to the left on the graph.
What is it?
(0.000106, 9.148)
3. To get a feel for how rapidly the natural log of x is falling as the x values are getting
closer to zero, fill in the table below.
Why do you think these points are not evident on the graph of
f
(
x
) =
x
ln
?
The yaxis is acting as a vertical asymptote. The calculator is unable to graph the
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This note was uploaded on 10/10/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.
 Fall '08
 GERMAN
 Calculus, PreCalculus

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