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Calculus: Secant Line approximating Tangent Line
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(a, f(a)) left parenthesis, "a" , "f" left parenthesis, "a" , right parenthesis , right parenthesis
a
,
f
a
Label:
equals
=
left parenthesis, 0.5 , 0.6 2 9 4 2 5 5 4 , right parenthesis
0
.
5
,
0
.
6
2
9
4
2
5
5
4
9
(a+h, f(a+h)) left parenthesis, "a" plus "h" , "f" left parenthesis, "a" plus "h" , right parenthesis , right parenthesis
a
+
h
,
f
a
+
h
Label:
equals
=
left parenthesis, 1.6 3 , 1.4 8 7 2 4 7 9 7 , right parenthesis
1
.
6
3
,
1
.
4
8
7
2
4
7
9
7
10
Expression 11: "a" equals 0.5
a
=
0
.
5
negative 10
−
1
0
10
1
0
11
a: left parenthesis, "a" , 0 , right parenthesis
a
,
0
Label:
equals
=
left parenthesis, 0.5 , 0 , right parenthesis
0
.
5
,
0
12
a+h: left parenthesis, "a" plus "h" , 0 , right parenthesis
a
+
h
,
0
Label:
equals
=
left parenthesis, 1.6 3 , 0 , right parenthesis
1
.
6
3
,
0
13
f(a) left parenthesis, 0 , "f" left parenthesis, "a" , right parenthesis , right parenthesis
0
,
f
a
Label:
equals
=
left parenthesis, 0 , 0.6 2 9 4 2 5 5 4 , right parenthesis
0
,
0
.
6
2
9
4
2
5
5
4
14
f(a+h) left parenthesis, 0 , "f" left parenthesis, "a" plus "h" , right parenthesis , right parenthesis
0
,
f
a
+
h
Label:
equals
=
left parenthesis, 0 , 1.4 8 7 2 4 7 9 7 , right parenthesis
0
,
1
.
4
8
7
2
4
7
9
7
15
Expression 16: "f" left parenthesis, "x" , right parenthesis equals sine left parenthesis, "x" , right parenthesis plus .3 "x"
f
x
=
s
i
n
x
+
.
3
x
16
Expression 17:
17
18
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powered by
(a, f(a))
(a+h, f(a+h))
a
a+h
f(a)
f(a+h)
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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