798
Answer Key
213 . 5 215 . 8/7 217 . DNE
219 . 2/3 221 . −4; 223 . Since −1≤cos(2 πx ) ≤1, then − x 2 ≤ x 2 cos(2 πx ) ≤ x 2 . Since lim x →0
x 2 =0= lim x →0
− x 2 ,
it follows that
x 2 cos(2 πx ) =0.
lim x →0
225 . [2, ∞] 227 . c =−1 229 . δ = ε 3 231 . 0m/sec Chapter 3 Checkpoint 3.1 . 1 4 3.2 . 6 3.3 . f ′(1) =5 3.4 . −32 ft/s 3.5 . P ′ (3.25) = 20 > 0; raise prices 3.6 . f ′( x ) =2 x 3.7 . (0, +∞) 3.8 . a =6 and b =−9
3.9 . f ″( x ) =2 3.10 . a ( t ) =6 t 3.11 . 0 3.12 . 4 x 3 3.13 . f ′( x ) =7 x 6 3.14 . f ′( x ) =6 x 2 −12 x . 3.15 . y =12 x −23 3.16 . j ′( x ) =10 x 4 ⎛ 3.17 . k ′( x ) = − 13
⎠ +(8 x +1) ⎛
⎞ ⎠ =56 x 6 +12 x 5 .
⎝ 4 x 2 + x ⎞
⎝ 2 x 5
(4 x −3) 2 .
3.18 . g ′( x ) =−7 x −8 . 3.19 . 3 f ′( x )−2 g ′( x ). 3.20 . 5 8 3.21 . −4.4 3.22 . left to right 3.23 . 3,300 3.24 . $2 3.25 . f ′( x ) =cos 2 x −sin 2 x 3.26 . cos x + x sin x cos 2 x 3.27 . t = π 3 , t = 2 π 3 3.28 . f ′( x ) =−csc 2 x
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