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lim-x-0-2-x-3-sin-1-x-tan-1-x-2-x-2-




Question Number 132137 by benjo_mathlover last updated on 11/Feb/21
  lim_(x→0) ((2/x^3 )(sin^(−1) x−tan^(−1) x))^(2/x^2 ) =?
limx0(2x3(sin1xtan1x))2x2=?
Answered by EDWIN88 last updated on 11/Feb/21
 L=lim_(x→0) ((2/x^3 )[(x+(x^3 /6)+(x^5 /(40)))−(x−(x^3 /3)+(x^5 /5))])^(2/x^2 )   L=lim_(x→0) ((2/x^3 )((x^3 /2)−((7x^5 )/(40))))^(2/x^2 )   L=lim_(x→0) (1−((7x^2 )/(20)))^(2/x^2 ) = e^(lim_(x→0) (−((14x^2 )/(20x^2 )))) =e^(−(7/(10)))
L=limx0(2x3[(x+x36+x540)(xx33+x55)])2x2L=limx0(2x3(x327x540))2x2L=limx0(17x220)2x2=elimx0(14x220x2)=e710

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