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Unformatted text preview: -«l\ Math 21A Kouba
Discussion Sheet 7 1.) Use the Intermediate Value Theorem to verify that the following equation is solvable, then use Newton’s Method to estimate the value of the solution to four decimal places :
(m — 1)3 = 10 + ./E 2.) Find the slope and concavity of the graph of my2 + y = 2 at a; = 0 and at as = 1 . Sketch the graph of this equation. 3.) The volume V of a sphere is changing at the rate of 7r ft.3/ min. At what rate is the
sphere’s surface area S changing when a.) S = 41r ft.2 ? ‘ b.) S = 367r ft.2 ? 4.) Find the height h and radius r of a right circular cone of maximum volume which can
be inscribed in a sphere of radius 1 ft. 5.) Car B is 30 miles directly east of car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph.
1 1 a.) At what rate is the distance between the cars changing after t = 5 hr. ? t = 5 hr. ?
b.) What is the minimum distance between the cars minimum distance occur ? and at what time t does the 6.) Assume that 1:2 + (5 — y)3 = 2m + 125 . d
a.) Find y’ = E: at the point (0,0) using implicit differentiation. b.) Solve the original equation for y. Then ﬁnd y’ = 21% at the point (0,0) using ordinary differentiation. ight 10 ft. and base radius 8 ft. Water begins 7.) A conical tank (point down) has he
3/ sec. At what rate is the depth h of the water ﬂowing into the tank at the rate of 1r ft.
changing a.) whenh = 1 ft. ? b.) whenh = 9ft. ? 8.) Assume that my2 = a: + tany . Write y” = d—g in terms of a: and y only . 1
9.) Use differentials to estimate the value of (9900); . 1 10.) The radius of a sphere is measured with absolute percentage error of at most 4%. Use
differentials to estimate the maximum absolute percentage error in computing the sphere’s a.) surface area. b.) volume.
The following problem is for recreational purposes only.
11.) Write a formula which will determine the nth term in the following list for n = 1, 2,
3, 4, 5, 6, . What is the 137th number in this list ?
5, 9, 13, 17, 21, 25, . . . ...
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