Download e-book for iPad: Advanced calculus; a text upon select parts of differential by Edwin Bidwell Wilson

By Edwin Bidwell Wilson

ISBN-10: 1172369704

ISBN-13: 9781172369706

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Additional resources for Advanced calculus; a text upon select parts of differential calculus, differential equations, integral calculus, theory of functions; with numerous exercises

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20. 22. 26. a , 2 2, _ 2 2K fa - x ; dx = ja h W = p A 24. fX0 fX0 1 ^nh2 CHAPTER 7 SECTION 1 , 2. page 306 x - | ( 5 - 9) y + 1 4. , , r, 60 x = Zi_L2 , 3y - 4 y ^o y 3 du CHAPTER 7 3y1/3 - 4 27 ^1/3 _ ^ , y ^ T + 3 -2y 3 10. x - 14. x = 18. yes 20. Suppose y i s i n t h e domain of g. "7, y + 7 y * -7 have g f - y ; = g [ - f f x j ] 22. 24. 28. i2. x « ry - ι ; 16. no Then y = f(x) = g[f(-x)] where x - g(y) · = - x = -g(y) We , so g i s odd. = g W 3 + g W so gfxj 3 = -gfxj + x. x = f[g(x)) 26.

Yes 20. Suppose y i s i n t h e domain of g. "7, y + 7 y * -7 have g f - y ; = g [ - f f x j ] 22. 24. 28. i2. x « ry - ι ; 16. no Then y = f(x) = g[f(-x)] where x - g(y) · = - x = -g(y) We , so g i s odd. = g W 3 + g W so gfxj 3 = -gfxj + x. x = f[g(x)) 26. 22 —. lo 1/5 Note t h a t f'(x) = 6 32 "10 3 * 4 * " 2 > 0 so t h e r e i s an i n v e r s e function. SU»'* = lim x(P^)mml x-K) = o since p/q 30. dx 32. z = (g o f ) (x) = 1 - 1/x so x = (go 0 = lim — — x-*0 other hand y = g (z) ffX(z) 34.

2π 12. 14. U w JÜL· Π 1+ 16. U 1+ u (\\ SECTION 7, 0 sin x page 194 2. e 6. 2x s i n x 4. cos x - 3 s i n x cos x 8. |(cos ypj/ç - cos x 42 CHAPTER 4 2 x csc 2 2 (tan x) 1 "\/7 x - j tan x)/x 10. -sec 14. 2 2 (cos x - sin x) ' = -2 cos x sin x - 2 sin x cos x 12. (x sec = -4 sin x cos x = -2 sin 2x, 2 2 (cos x - sin x)' = (cos 2x)' = -2 sin 2x. 16. x sin x - 20 cos x 18 . LHS = 1 + sec x tan x - sec 2 2 x = sec x tan x - tan tan x sec x + tan x 1 sin x 1 + (1/sin x) 1 + sin x * tan x(sec x - tan x) = 1 1 + (sec x/tan x) x 20.

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Advanced calculus; a text upon select parts of differential calculus, differential equations, integral calculus, theory of functions; with numerous exercises by Edwin Bidwell Wilson


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