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# UCR - MATH 009B - Study guide for finals 6.4-7.4 - Study Guide

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UCR - MATH 009B - Study guide for finals 6.4-7.4 - Study Guide

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Unformatted text preview: 16.5 Partial fraction Decompositron (PAD) function be where tbe degree of p * Find A, B, or c of a his less than the degree of q (x-a) Lax) where ex-a)" 13. la Forms. Linear Jerms" decomposition of the highest power of Cx-a), then Ex: 3x+5 A B A(x+3) + B(x+1 = 3x+5 XP-3, 31-345 = 163+3) -4 = 0 - 23 B.(-3+) 1 X-D-L, 3(-1)+5= AC-3) + e 2 = 2A * Make A or B 2000 to Selve for or 5 -2 -2 12b I =Al Study Soup is Quadratic Tims. (x2+bx+)/903.) whest (x? +bx+c) the highest power of x'+bx+c, then decompositron is. B, X+ C B , X + 2 + BaxtCo .... *+bx c * (x2+bx+c)? (x2+bx+se A Study SoupEX (X-1)(x +*+1) is A BX + written as (-1) (x-D-D uses A, B, C & X+X+ Ferd C X? +x+D uses. Bxtc CX3 - 24% -60 notice boxsprafesorden 72 - X-4 Hust perfon polynomial since (too complicated to solve) 6.6 Hyperbolic Functions 1 coshk), e tee 4. Sech(x) = coshers 2. Sinb(x); ece 3. tanb(x)= cookies s cscha) - Sinh(x) tos nex) 6. Cotho) Sinh (*) Basic identities: 2 4) Cush(Sinb(x) = 1 3) Coth?(X) + esch?(x) .1_ 5) Sinh(zx) - 2 Sinh (x) cosh (x) ) tanb?(X) + Sech?(x) = 4) cosh(2x) = cosh?(x) + Sinh?(x) Tax Ssechel 4t- tanh(u du U=7-3. du = 7dt, dydt =tanh( 74-3) + @ coshoes) - ette o le sinha) Ho derive et ex cbrings down coefficient. f ) S.cos(x) -> Set eba fettet ekrefsinh ) +C6.8 Improper Integral De finition.converge or Diverge 1) let t be continuous function on La,co). Deline T f (x) dx to be tim fold 2) Let f be continuous function on coob Define f food to be tim e La ca todx 3 Let f be a continuous function on C-00,00). Letc be any co number: define f(x) dx to be fim a> - Am rb b-pc +6dx Stuch Soup * converge) = limit exists / Divergel - Limit does not exist *> lim dx b-04 X Side Note =--() = 1 (b hosino valve) la is a number o yob Serves as Exal for 2) In ex dx = limon la exdx = ex la infinite number Tim do Sto Soup alime tan 18 + lima tanto = (0-1)+(-o):17] I dea: If either a orbis INFINITE , then use limit to compute & f&dx or if f(x) "=" for some x in [a,b] needs to use limit. ( usually happens with 6 ) Definition #zly Infinite Range FO) is continuous on [a, b] except at ciascab where | XEC is the asymptote of f

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