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lim-x-6x-8x-2-2x-3-4x-5-x-6-x-3-4x-5-1-6-x-




Question Number 130176 by liberty last updated on 23/Jan/21
 lim_(x→∞)  ((6x+(√(8x^2 −(√(2x^3 +(√(4x^5 )))))))/( ((x^6 −x^3 +(√(4x^5 ))))^(1/6)  + x))=?
limx6x+8x22x3+4x5x6x3+4x56+x=?
Answered by EDWIN88 last updated on 23/Jan/21
 lim_(x→∞)  ((6x+(√(8x^2 −(√(2x^3 +2x^2 (√x))))))/( ((x^6 −x^3 +2x^2 (√x)))^(1/6)  +x)) =   lim_(x→∞)  ((6x+(√(8x^2 −x(√(2x+2(√x))))))/(x ((1−x^(−3) +2x^(−4) (√x)))^(1/6)  +x)) =   lim_(x→∞)  ((x (6+(√(8−x^(−1) (√(2x+2(√x))))) ))/(x(((1−x^(−3) +2x^(−4) (√x)))^(1/6)  +1))) =   ((6+(√8))/2) = 3+(√2)
limx6x+8x22x3+2x2xx6x3+2x2x6+x=limx6x+8x2x2x+2xx1x3+2x4x6+x=limxx(6+8x12x+2x)x(1x3+2x4x6+1)=6+82=3+2

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