Answer Key
817
4.29 . y = 3 2 x 4.30 . The function f has a cusp at (0, 5)
f ′( x ) =−∞. For end behavior,
lim x →0 +
f ′( x ) =∞,
lim x →0 −
lim x →±∞ f ( x ) =−∞. 4.31 . The maximum area is 5000ft 2 . 4.32 . V ( x ) = x (20−2 x )(30−2 x ). The domain is [0, 10]. 4.33 . T ( x ) = x 6 + (15− x ) 2 +1 2.5 4.34 . The company should charge $75 per car per day. 4.35 . A ( x ) =4 x 1− x 2 . The domain of consideration is [0, 1]. 4.36 . c ( x ) = 259.2 x +0.2 x 2 dollars
4.37 . 1 4.38 . 0 4.39 . lim
x →0 + cos x =1. Therefore, we cannot apply L’Hôpital’s rule. The limit of the quotient is ∞
4.40 . 1 4.41 . 0 4.42 . e 4.43 . 1
4.44 . The function 2 x grows faster than x 100 . 4.45 . x 1 ≈ 0.33333333, x 2 ≈ 0.347222222 4.46 . x 1 =2, x 2 =1.75 4.47 . x 1 ≈ − 1.842105263, x 2 ≈ − 1.772826920 4.48 . x 1 =6, x 2 =8, x 3 = 26 3 , x 4 = 80 9 , x 5 = 242 27 ;
x * =9
4.49 . −cos x + C 4.50 . d dx (
x sin x +cos x + C ) = sin x + x cos x −sin x = x cos x
x 3 + 1 2
4.51 . x 4 − 5 3
x 2 −7 x + C
4.52 . y = − 3 x +5
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