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appendix_a

# appendix_a - APPENDIX Quadratic Formula Ifax2 bx c=0,thenx...

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Unformatted text preview: APPENDIX Quadratic Formula Ifax2+bx+c=0,thenx Hyperbolic Functions sinh x = X —X cosh x Trigonometric Identities sin26 + c0526 = 1 e —e —2 , A E, csc6i— B E, sec6 A E, cot6 Mathematical Expressions —b :t b2 — 4ac _ 2a X + —X = %, tanh x = C A sin(6 :t 45) = sin 6 cos d) :l: cos 6 sin (15 sin 26 = 2sin6cos6 cos(6 i (1)) = cos 6 cos (1) ¥ sin 6 sin qb cos 26 = cos2 6 — sin2 6 1 + cos 26 , 1 — cos 26 cos6=i —2—, s1n6=i —2— tan6 = 1+ tan26 = S€C20 sin 6 cos 6 Power-Series Expansions x3 Slnx=x—§+ —1 x2+ cosx~ 2! 440 1 + cot26 = c5026 x3 smhx=x+§+ h —1+x2+ cos x— 2! - sinh x cosh x Derivatives i n _ n—lil’i dx(u ) _ nu dx i(1w) — uﬂ + vﬂ dx dx dx vd_u _ “a i<z> _ dx dx dx ’U 02 d _ 2 du dx (cot u) — csc udx d du — 56C” = tanusecu— ( ) dx i(cs ) - —c cot uﬂ dx c u so u dx 1(sin u) — cos 14% dx dx d (cos u) s n u d” _ : _ 1 _ dx dx d _ 2 du dx(tan u) — sec udx d _ _ du 5(smh u) — coshudx d . du 3(cosh u) — smhudx APPENDIXA Mathematical Expressions - 441 Integrals x"“ dx 2% +‘bx "d = + 7b —1 ——=—+C Ix x "+1 C,” JVa+bx b dx 1 xdx 2 2 Z _ + + — = \/ :1: a + C [a + bx b1n(a bx) C J x2 i a2 x dx 1 a + x —ab d 1 = 1n + C, b < 0 x z _ ‘ / 2 [a + bx2 2‘V—ba [a — x —ab] a [W valn[ a + bx + cx xdx 1 2 :_ b ba+bx2 2b1n<bx+a)+C’ +x\/E+2\/E]+C,c>0 )6de x a xVab 1 _2 _b = tan‘1 + C, ab > 0 = ' -1 —Cx Ja+bx2 b bVab a V_—csm <m>+ac>0 dx 1 a + x baz—x2=gln[a—x]+c’ a2>x2 Isinxdx=—cosx+C 2 J'Va+bxdx=§g\/(a+bx)3+C [cosxdx=sinx+C — — \/ 3 1 x , JxVa + bx dx = W + C chos(ax) dx = geoswx) + Esm(ax) + C 2x WWW z + C V c°s<ax> dx = 705% 105b3 02x2 _ 2 + ——sin(ax) + C 1 / 1 , /— 3 J aZ—xzdx=§[x a2—x2+azsin_1%]+C, a>0 a eaxdx + C 1 a JxV a2 — x2 dx = —§ (a2 — x2)3 + C sz 02 — x2 1 JVxZ i azdx = §[x\/x2:t a2 :i: a21n(x + x2 :l: a2)] +C + = (xzia2)3+C x 2 23 “2 2 2 =2 (xia):F—x xia a4 —-8-1n(x+ xzia2)+C eax xe‘” dx = yum — 1) + C sinhxdx = coshx + C coshxdx = sinhx + C ...
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