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Question-167593

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Question Number 167593 by cortano1 last updated on 20/Mar/22
Answered by qaz last updated on 20/Mar/22
A=lim_(x→0) (((√(17−2(x+2)^2 ))∙((3(x+2)^3 +3))^(1/3) −9)/x^2 ) =lim_(x→0) (((√(9−2x^2 −8x))∙((3x^3 +18x^2 +36x+27))^(1/3) −9)/x^2 ) =9lim_(x→0) (((√(1−(8/9)x−(2/9)x^2 ))∙((1+((36)/(27))x+((18)/(27))x^2 +(3/(27))x^3 ))^(1/3) −1)/x^2 ) =9lim_(x→0) ((ln((√(1−(8/9)x−(2/9)x^2 ))∙((1+((36)/(27))x+((18)/(27))x^2 +(3/(27))x^3 ))^(1/3) ))/x^2 ) =9lim_(x→0) (((1/2)ln(1−(8/9)x−(2/9)x^2 )+(1/3)ln(1+((36)/(27))x+((18)/(27))x^2 +(3/(27))x^3 ))/x^2 ) =9lim_(x→0) (1/(2x))[((−(8/9)−(4/9)x)/(2(1−(8/9)x−(2/9)x^2 )))+((((36)/(27))+((36)/(27))x+(9/(27))x^2 )/(3(1+((36)/(27))x+((28)/(27))x^2 +(3/(27))x^3 )))] =9lim_(x→0) (1/(2x))∙(((−4−2x)/(9−8x−2x^2 ))+((12+12x+3x^2 )/(27+36x+28x^2 +3x^3 ))) =9lim_(x→0) (((−4−2x)(27+36x+28x^2 +3x^3 )+(12+12x+3x^2 )(9−8x−2x^2 ))/(2x(9−8x−2x^2 )(27+36x+28x^2 +3x^3 ))) =9lim_(x→0) (((−4∙36−2∙27+12∙9−12∙8)x+o(x))/(2∙9∙27x+o(x))) =−((31)/9)
A=limx→017−2(x+2)2⋅3(x+2)3+33−9x2=limx→09−2x2−8x⋅3x3+18x2+36x+273−9x2=9limx→01−89x−29x2⋅1+3627x+1827x2+327x33−1x2=9limx→0ln(1−89x−29x2⋅1+3627x+1827x2+327x33)x2=9limx→012ln(1−89x−29x2)+13ln(1+3627x+1827x2+327x3)x2=9limx→012x[−89−49x2(1−89x−29x2)+3627+3627x+927x23(1+3627x+2827x2+327x3)]=9limx→012x⋅(−4−2x9−8x−2x2+12+12x+3x227+36x+28x2+3x3)=9limx→0(−4−2x)(27+36x+28x2+3x3)+(12+12x+3x2)(9−8x−2x2)2x(9−8x−2x2)(27+36x+28x2+3x3)=9limx→0(−4⋅36−2⋅27+12⋅9−12⋅8)x+o(x)2⋅9⋅27x+o(x)=−319
Answered by cortano1 last updated on 20/Mar/22
A= lim_(x→2) (((17−2x^2 )(((3x^3 +3)^2 ))^(1/3) −81)/([(√(17−2x^2 )) ((3x^3 +3))^(1/3) +9 ](x−2)^2 )) A= (1/(18)) lim_(x→2) ((−4x (((3x^3 +3)^2 ))^(1/3) +(17−2x^2 )((2.(9x^2 ))/(3 ((3x^3 +3))^(1/3) )))/(2(x−2))) A=(1/(36)) lim_(x→2) (((((17−2x^2 )6x^2 )/( ((3x^3 +3))^(1/3) )) −4x (((3x^3 +3)^2 ))^(1/3) )/((x−2))) A= (1/(36)) lim_(x→2) (((17−2x^2 )6x^2 −4x(3x^3 +3))/((x−2) ((3x^3 +3))^(1/3) )) A=(1/(108)) lim_(x→2) ((102x^2 −24x^4 −12x)/((x−2))) A= (1/(108)) lim_(x→2) ((204x−96x^3 −12)/1) A= ((408−768−12)/(108)) = − ((31)/9)
A=limx→2(17−2x2)(3x3+3)23−81[17−2x23x3+33+9](x−2)2A=118limx→2−4x(3x3+3)23+(17−2x2)2.(9x2)33x3+332(x−2)A=136limx→2(17−2x2)6x23x3+33−4x(3x3+3)23(x−2)A=136limx→2(17−2x2)6x2−4x(3x3+3)(x−2)3x3+33A=1108limx→2102x2−24x4−12x(x−2)A=1108limx→2204x−96x3−121A=408−768−12108=−319

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