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CHAPTER 2 2.1
LIMITS AND CONTINUITY
RATES OF CHANGE AND TANGENTS TO CURVES
1. (a)
f
f (3)f (2) x
2. (a)
f
289
19
32
1
g (3) g (1)
3 ( 1)
31
2
g x
f (1)f (1)
(b) x
g
2
(b)
x
3. (a)
4
t
g
5. R
6. P
4
0
20
811
(b)
2
0 3
3 3
6
g () g () ()
3
(21)(21) 2
0
1
(81610)(145)
22 0
1
2
2
44h h 2 51
h
h
4h h 2 h
4 h. As h 0, 4 h 4 at P(2, 1) the slope is 4.
2
2
(7(2h ) )(72 )
x
744h h 2 3
h
h
4hh 2 h
4 h. As h 0, 4 h
is 4. (b)
0
y (1) 4( x 2) y 1 4 x 8 y 4 x 9
y
8. (a)
31
((2h ) 5)(2 5)
x
(b) t
6
6
g
2
2
21
y
7. (a)
h
2
2
0
P (2) P (1)
h
2
(21)(21)
R(2) R(0)
h
88
4 ( 2)
(b) t
g () g (0) t
4
3 4
4. (a)
11
4
1
2
g (4) g ( 2)
h3 h h
20
1(1)
y 3 (4)( x 2) y 3 4 x 8
y 4 x 11
4 at P(2, 3)
the slope