By George B. Thomas, Maurice D. Weir, Joel Hass
Instructor's ideas handbook for Thomas' Calculus, twelfth version.
This comprises either the only Variable and Multivariable chapters which are occasionally divided into separate books. includes recommendations for ALL difficulties, even and odd.
Text are available the following: http://bibliotik.org/torrents/63092
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Additional resources for Thomas' Calculus: Instructor's Solutions Manual (12th Edition)
3. If f is odd and defined at x, then f(cx) œ cf(x). Thus g(cx) œ f(cx) c 2 œ cf(x) c 2 whereas cg(x) œ c(f(x) c 2) œ cf(x) b 2. Then g cannot be odd because g(cx) œ cg(x) Ê cf(x) c 2 œ cf(x) b 2 Ê 4 œ 0, which is a contradiction. Also, g(x) is not even unless f(x) œ 0 for all x. On the other hand, if f is even, then g(x) œ f(x) c 2 is also even: g(cx) œ f(cx) c 2 œ f(x) c 2 œ g(x). 4. If g is odd and g(0) is defined, then g(0) œ g(c0) œ cg(0). Therefore, 2g(0) œ 0 Ê g(0) œ 0. 5. For (xß y) in the 1st quadrant, kxk b kyk œ 1 b x Í x b y œ 1 b x Í y œ 1.
Thus choose the smaller distance, $ œ %% c %# . ¹È4 c x c 2¹ % Ê c% È4 c x c 2 % Ê 2 c % È4 c x 2 b % Ê (2 c %)# % c x (2 b %)# Ê c(2 b %)# x c 4 c(2 c %)# Ê c(2 b %)# b % x c(2 c %)# b %. k x c 0k $ Ê c $ x $ . Then c$ œ c(2 b %)# b 4 œ c%# c %% Ê $ œ %% b %# , or $ œ c(2 c %)# b 4 œ 4% c %# . Thus choose the smaller distance, $ œ 4% c %# . For x Á 1, kx# c 1k % Ê c% x# c " % Ê " c % x# " b % Ê È1 c % kxk È1 b % Ê È" c % x È1 b % near B œ ". kx c 1k $ Ê c$ x c 1 $ Ê c$ b " x $ b ".
Yacxb œ acxb& c acxb$ c acxb œ cx& b x$ b x œ cyaxb. Odd. 11. yacxb œ " c cosacxb œ " c cos x œ yaxb. Even. 12. yacxb œ secacxb tanacxb œ 13. yacxb œ acxb% b" acxb$ c#acxb œ x% b" cx$ b#x sinacxb cos# acxb œ csin x cos# x œ csec x tan x œ cyaxb. Odd. % b" œ c xx$ c# x œ cyaxb. Odd. 14. yacxb œ acxb c sinacxb œ acxb b sin x œ cax c sin xb œ cyaxb. Odd. 15. yacxb œ cx b cosacxb œ cx b cos x. Neither even nor odd. 16. yacxb œ acxbcosacxb œ cx cos x œ cyaxb. Odd. 17. Since f and g are odd Ê facxb œ cfaxb and gacxb œ cgaxb.