Analytical Geometry And The Calculus – Aw Goodman

f vse tanydy. 32. [si Vx dx. 34. [ee 35. [ee 1 — tan? z 1 —e* oW/. fo sec? 6 dé. 38. fui — cos 6 dé. 40. f sin sin 38 ae 41. f sins sin x dx. 43. f cane + cot 0)? dé. 44. few sin bx dx. Tan-1 46.

ata a 47. { cos (In x) dx. l+y 49. f tant (In x) dx. 50. | e® sinh x cos x dx. * cos? x dx 53. 52, f eae sin 89 + 2 cos sin 26 cos 56 dé * a ~ sec40 58. x55, if sin @ + 7 cos @ jg 56.

Hf eos 6 sin’86 de. cos? ¢ tan? ¢ sec? t ee Hf csc t (In x) AK = Set cosud 4 n> [ny oW = e! SER uz 4, dy : Bee vA 33. 36. 42. 48. oR 54. eh: *60. f 00s NI AXe 3. f [ hy oe diving cab. sf lie ees Review Problems 8e” dx 3 4 2e” — 1 e2″)) tan x dx In (cos x)” 24 dx x(x? — 1)(x? — 4) sin 6 cos?

6 d@ Pe sin2g) ee neve |

Similarly, the velocity of a moving particle has a magnitude (called its speed) and a direction, the direction in which the particle is moving. Initially the theory of vectors was constructed to handle problems involving forces and velocities. It is quite natural to represent a force (or a velocity) by a directed line segment (an arrow). The length of the line segment is the magnitude of the force (or the speed of the moving particle).

fw a uk +04 # tanu = sec? wt. dx d*y _ dy d?x 2 ne dp dt dt? ~~ dt dt KS EO _—_., pe cot u = —csc2 ue. ds (FZ ) Hs (2 Ve du dx dx os x ie wry dx v o d du : === See = SSC Hain Wi — d the dx dx — log, u = —— log, e dx 1 dx d Bey == SOY S|] SCS COL Wi a in login dx dx dx wildy Cylindrical Coordinates Polar Coordinates Spherical Coordinates aV = rdrdé dz.

Kia COs O, tai dV = p* sing do dg dé, y= sind, “irs dé OS ar rede: CAF ar dy. Vectors ds d*s ds \ dt a a a grad f= Vf= f,i+ f,i + 7k: fp) Review Formulas ER Oe hd ae _ ac ped, ac ad+be a/b ad at Aaa bd bd b bd’ Fah? pag ed Ca Be —@ a : —h+ /h2 — ie oe Ses aE ax?

+ bx +c=0 has roots oe a a= b= (a— bya-+ b). a? — b3 = (a — b)(a? + ab + b?). ata’ = a”, guppy = (ab). (a”) ee Wa” = (Wa)”. qe! = ie ae = a sin 6 cos @ | be = tang, – = té. : = ; cos sin 6 ste cos 6 a sin 6 oe sin?

9 + cos? @ = 1. sec? @ — tan? 6 = 1. sin (A + B) = sin Acos B + cos A sin B. sin (A — B) = sin A cos B — cosA sin B. cos (A + B) = cos Acos B — sin A sin B. cos (A — B) = cosAcos B + sin A sin B. csc?

6 — cot? é@ = 1. sin (z = 4) =——COSEA T , 8 AG cos (3 ) sin 7 t — — A} = cota. an (2 ) O Sin2/Al— 2 sin ArcosiA 2 tant (4 4 BY = tan A + tan B 1 — tan 4 tan B cos 2A = cos?

A — sin? A. tan (A — B)= Mae Ane : tan 2A = ene cos A cos B = + [cos (A + B) + cos(A — B)], COs7-A = fant sin A sin B = F [cos (A — B) — cos(A + B)]. sin A cos B = Lsin (A + B) + sin(A — B)], ees Analytic Geometry and the Calculus Digitized by the Internet Archive in 2022 with funding from – Kahle/Austin Foundation https://archive.org/details/analyticgeometryOO00awgo_ 3rdedition Analytic Geometry ANG {he CALCULUS sic cams A.

W.

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