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lim-x-x-x-2-3x-2-2022-x-x-2-5-2022-x-2022-

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Question Number 162182 by bobhans last updated on 27/Dec/21
lim_(x→∞) (((x−(√(x^2 −3x+2)) )^(2022) +(x−(√(x^2 −5)) )^(2022) )/x^(2022) ) = ?
limx→∞(x−x2−3x+2)2022+(x−x2−5)2022x2022=?
Answered by cortano last updated on 27/Dec/21
lim_(x→∞) (((x−x(√(1−3x^(−1) +2x^(−2) )) )^(2022) +(x−x(√(1−5x^(−2) )) )^(2022) )/x^(2022) ) = lim_(x→∞) (((1−(√(1−3x^(−1) +2x^(−2) )) )^(2022) +(1−(√(1−5x^(−2) )) )^(2022) )/1) = 0
limx→∞(x−x1−3x−1+2x−2)2022+(x−x1−5x−2)2022x2022=limx→∞(1−1−3x−1+2x−2)2022+(1−1−5x−2)20221=0

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