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Unformatted text preview: .5 to sketch the curve. 19. y s xl 13. lim |||| 21. y s 2 xl0 1
x2 2 20. y s Evaluate the limit.
ln 1 1 0,
1, 3 s 0 _1 2, 1 sin 2 x, s |||| xl0 y 0, 4
_2 2 s 7. lim , 2 x 6. f x 7–14 x
x (c) Sketch the graph of f .
(d) Sketch a possible graph of f . 0, 4 x2 5. f x s sx, x 4. f x x 3, 27x s s s 18. The ﬁgure shows the graph of the derivative f of a function f . (a) On what intervals is f increasing or decreasing?
(b) For what values of x does f have a local maximum or
minimum? 1 1 e1 x .
(b) Explain the shape of the graph by computing the limits of
, 0 , and 0 .
f x as x approaches ,
(c) Use the graph of f to estimate the coordinates of the inﬂection points.
(d) Use your CAS to compute and graph f .
(e) Use the graph in part (d) to estimate the inﬂection points
more accurately. 40. (a) Graph the function f x C HAPTER 4 REVIEW C AS C AS 41. If f x arctan cos 3 arcsin x , use the graphs of f , f , and
f to estimate the x-coordinates of the maximum and minimum
points and inﬂection points of f . 56. Do Exercise 55 when CD ln 2 x x sin x , use the graphs of f , f , and f to
estimate the intervals of increase and the inﬂection points of f
on the interval 0, 15 . 2 c xe c x . What happens to the maximum and minimum points and the inﬂection
points as c changes? Illustrate your conclusions by graphing
several members of the family. 45. Show that the equation x 101 x 51 x 1 2 fx 5 for all x in 0, 4 . Show that 9 shape of a right circular cylinder surmounted by a hemisphere.
What dimensions will require the least amount of metal?
59. A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket price set at $12, average
attendance at a game has been 11,000. A market survey indicates that for each doll...
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- Fall '07