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f ( x + h ) − f ( x)
We will calculate the limit limh→0
to get the general formula for the
h
√
slope of the tangent line for f (x) = x. Then, we will plug in x = 9 to this formula to
1 2 get the slope of the tangent line at the point (9, 3).
√
√
f ( x + h ) − f ( x)
x+h− x
lim
= lim
,
h→ 0
h→ 0
h
h
√
√√
√
( x + h − x)( x + h + x)
√
= lim
,
√
h→ 0
h ( x + h + x)
( x + h) − x
= lim √
√,
h→ 0 h ( x + h +
x)
1
= lim √
√,
h→ 0
x+h+ x
1
= √.
2x
1
1
Therefore, the slop of the tangent line at the point (9, 3) is √ = .
6
29
1
Next, since this tangent line has slope , and it passes the point (9, 3), by the point6
1
1
3
slope formula, the tangent line equation is y − 3 = (x − 9). That is, y = x +
6
6
2...
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This note was uploaded on 02/10/2014 for the course MATH 235 taught by Professor Lucas during the Fall '08 term at James Madison University.
 Fall '08
 LUCAS
 Calculus, Logic

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