During this witty assortment you can find quotations grouped in different types that replicate the variety of human life, hopes, and achievement:
Life and dying (And a few of What occurs in Between)
“Let us no longer glance again in anger, nor ahead in worry, yet round in awareness.”
Love and Friendship
“The middle has its purposes of which cause understands nothing.”
Success and how you can in attaining It
“Success is the facility to move from one failure to a different without lack of enthusiasm.”—Sir Winston Churchill
The lifetime of the Mind
“Don't speak except you could increase the silence.”
—Jorge Luis Borges
Politics and Politicians, govt and Statesmen
“Nothing in lifestyles is sure other than demise and taxes.”
“Joy shared is two times the enjoyment. Sorrow shared is part the sorrow.”
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Extra resources for 1001 Smartest Things Ever Said
6! 5) 3: etg x = 1 + x + x2 3x3 9x4 37x5 + + + +... 2! 3! 4! 5! 216 1: earcsin x = 1 + x + x2 2x3 5x4 + + +... 2! 3! 4! 7) 2: earctg x = 1 + x + x2 x3 7x4 ¡ ¡ +... 2! 3! 4! 217 1: ¼ 1 P e¼x + e¡¼x 1 1 = + 2x (cf. 421 3. ): ¼x 2 2 ¡¼x e ¡e x k=1 x + k Printed from Table of Integrals, Series, and Products CD-ROM. Copyright © 1996 by Academic Press, Inc. All rights reserved. 421 2: e¼x 1 P 2¼ 1 1 = + 2x (¡1)k 2 ¡¼x ¡e x x + k2 k=1 (cf. 422 3. 231 1 P k=0 akx = 1 1 ¡ ax [a > 1 and x<0 or 0 0]: Printed from Table of Integrals, Series, and Products CD-ROM.
Is called a power series. 311 1. converges absolutely and outside this circle, it diverges. This circle is called the circle of convergence and its radius is called the radius of convergence. If the series converges at all points of the complex plane, we say that the radius of convergence is infinite (R = +1). 312 Power series may be integrated and differentiated termwise inside the circle of convergence; that is, Z x » ½ 1 P ¾ 1 P ak (x ¡ »)k+1 ; dx = k + 1 k=0 ½1 ¾ k=0 1 P P d k ak (x ¡ ») kak (x ¡ »)k¡1 : = dx k=0 k=1 ak (x ¡ »)k 18 The radius of convergence of a series that is obtained from termwise integration or differentiation of another power series coincides with the radius of convergence of the original series.
All rights reserved. 421 2: e¼x 1 P 2¼ 1 1 = + 2x (¡1)k 2 ¡¼x ¡e x x + k2 k=1 (cf. 422 3. 231 1 P k=0 akx = 1 1 ¡ ax [a > 1 and x<0 or 0 0]: Printed from Table of Integrals, Series, and Products CD-ROM. Copyright © 1996 by Academic Press, Inc. All rights reserved. 30 Introduction The trigonometric and hyperbolic sines are related by the identities sh x = 1 sin (ix); i sin x = 1 sh (ix): i The trigonometric and hyperbolic cosines are related by the identities ch x = cos (ix); cos x = ch (ix): Because of this duality, every relation involving trigonometric functions has its formal counterpart involving the corresponding hyperbolic functions, and vice-versa.