5. What appears to be the limit as Ax→0?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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#5 Please

1. Graph the function h(x) = (x + 1)2 + 2. Plot the point (1, 2) on your graph.
2. Fill in the chart for each of the following: Let x = 1
Ax
2
1.5
1
.5
-.5
x+Ax
F(x+Ax)
3. Using different colors draw secant lines from (1,2) to each of the points
(х+Дх, F(x+Дх)).
4. Calculate the difference quotient for each of these secant lines. Insert the calculated values
in the last row of the chart in #2.
F(x + Ax) – F(x)
((х + Дх) — х)
5. What appears to be the limit as Ax->0?
6. As Ax->0, the graph becomes a tangent line and not a secant line. What is the difference
between these two types of lines?
7. Now use the general form for the difference quotient with our function
f(x)
x2 – 2x + 3 to simplify the formula:
f(x + Дх) — f(x)
f'(x) = lim
Дх--0
Дх
8. What do you notice about the original f(x) and f'(x)?
Transcribed Image Text:1. Graph the function h(x) = (x + 1)2 + 2. Plot the point (1, 2) on your graph. 2. Fill in the chart for each of the following: Let x = 1 Ax 2 1.5 1 .5 -.5 x+Ax F(x+Ax) 3. Using different colors draw secant lines from (1,2) to each of the points (х+Дх, F(x+Дх)). 4. Calculate the difference quotient for each of these secant lines. Insert the calculated values in the last row of the chart in #2. F(x + Ax) – F(x) ((х + Дх) — х) 5. What appears to be the limit as Ax->0? 6. As Ax->0, the graph becomes a tangent line and not a secant line. What is the difference between these two types of lines? 7. Now use the general form for the difference quotient with our function f(x) x2 – 2x + 3 to simplify the formula: f(x + Дх) — f(x) f'(x) = lim Дх--0 Дх 8. What do you notice about the original f(x) and f'(x)?
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