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Unformatted text preview: Math 41 Fall 2005 Practice Exam 2 . Differentiate each of the following functions. sin w (a) y = 9:
(b) f(Z) = 008((1nzl2)
(0) g(t) = A arcsin(Bt + C) . Evaluate the following limits. If there is an inﬁnite limit, then determine whether it is
00 or —oo. _ 1 — cos 6
(a) £133 ”—92—
(b) lin(1)(e”c + 201/5”
. . . . 127T
. Use a linear approxnnation to estimate cos E .
127r 7r 7r
H' t: — = — — —.
m 25 2 50
. The linear density of a thin rod a distance :1: cm from the end is 1 + 2 g/ cm. What
a: is the total mass of the ﬁrst 1 cm of the rod? . Find an equation for the tangent line to the curve
3:3 + :3 tan‘1 3/ = 86y at the point (2,0). . A box with a square base is taller than it is wide. In order to be sent trhough the US.
mail, the height of the box and the perimeter of the base can add up to at most 108
in. What is the maximum volume for such a box? . Coffee is poured at a constant rate of 20 cm3/s into a mug Whose inside is shaped like
a truncated cone (see the ﬁgure). The radius of the top of the mug is 4 cm, the radius
of the bottom of the mug is 2 cm, and the height of the cup is 6 cm. How fast will the
coffee level be rising When the coffee is halfway up? 8. Determine graphically What happens if Newton’s method is used for the function Whose
graph is shown with the initial approximation x0 = 3. 9. Consider the function f (x) = 61/9” (a) Find all asymptotes of f. (b) Find f’ and f”. (c) Find on What intervals f is increasing and decreasing. (d) Find on What intervals f is concave up and concave down. (e) Using What you’ve found above, sketch the graph of f. Label all local extrema
and inﬂection points. ...
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