6.3 Completed Notes.pdf

6.3 Completed Notes.pdf - A Partial Fractions Examples 3 11...

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Unformatted text preview: A. Partial Fractions Examples: 3.. 11* “I“ w 7 71%“‘”“ nETI-ﬂm I16] *C W Desiré Tayfor Math 1242 ww’“ 3 x—l dx -’l 2') I(x+1ixz+x+li 2‘ .______ »; FZJnIx-HJ +S~leow [, 4.2mm“! 4—,bn I»! *L -: azﬁxvx lxw) 4—.914 lxl+x+ll +a 330 'P , "gurgﬁ‘d ) dx (See Power Rule: Stewart page 323.) W (by - a [ 3114'5 ___ ___”: + B 4' JG? 2 .. _, «z I (go-2) 2( x+ a) X#2 [x 2) X+ l;g:§¥”1(§§5(9.3 + ch—g'fiﬂivf’i 55¢] , Xg—l W A's B 2. “mus -; A (o) 1' ace) H 0+2) B. Other Techniques: Formulae 1 u du=—tan'l _ +C 3'? J‘uz+az a (a) *- Examples: 1 I 1* 5’ _“‘ -- 4a...“ ——»—-" )+—L / c x a :3 W a» =1 ’ 1 ,- l S ’ 00A 2’ J4x2+9dx f aura" Desiré Taylor Math 1242 . | i | i 3 6. Long Division Perform long division when degree of numerator 2 degree of denominator. ‘ Examples: Y ,4 1.) I; 461x x441 Fiﬁ-m:- k5} , .43. ”ﬂex! ,Sx,q+x+q00)< ‘4'“ v A“ + x-% Ml L” 7613c» ... 303/4: Mowers) IB'; 2. 9 x: 3 M15 3533-4: A(’b-+’3—l)'+ 5(0) 77:77! 5 Desiré Taylor Math 1242 XI- D. Completing the Square If a quadratic expression x2 + bx + c has the qualit C = Y Examples: 1.) Complete the square: )62 +6x+13= (anti—)1: (if) : (3)190! G+QX+Q> +l5 Desiré Taylor Math 1242 b 2 x2+bx+c=[x+—— 2 J then it will factor into a perfect square: Webwork 8. (1 pt) Extra Problem 1 Evaluate the integral ] Desiré Taylor 9x—5 x2+9 (1).: S 01 _, ML 36%“ x94 “x144 “(ext 05? MFQKOD?‘ 0%de {Lowcxobc l .4 * LL 0] ,_ «*5!» (3)) z .5,- AW 6(3 Math 1242 ...
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