X2+x-2/x2-1 Lim=1?

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  • Lim. x → 1: [(x² + x - 2)/(x² - 1)]

    By reason of factorisation, we have

    Lim. x → 1: [(x + 2)(x - 1)/(x + 1)(x - 1)]

    = Lim. x → 1: [(x + 2)/(x + 1)]

    By direct substitution, we have

    (1 + 2)/(1 + 1)

    = 3/2

    Therefore, Lim. x → 1: [(x² + x - 2)/(x² - 1)] = 3/2 ...Ans.

  • khalil
    Lv 7
    2 years ago

    you did mention ...where the x goes

    if x → 1 then the f(1) → 0/0

    hopital rule ... der top / der bottom

    (2x + 1) / 2x

    x → 1

    the answer is 3/2 ◄◄◄

    ▬▬▬▬

    if x → ∞ then

    coefficient of higher on the top / coefficient of higher on the bottom

    1/1

    the answer is 1 ◄◄◄

  • ted s
    Lv 7
    2 years ago

    x² + x -2 = [x + 2 ] [ x - 1 ] & x² - 1 = [ x + 1 ] [ x - 1 ]...thus the ratio approaches 3/2 as x approaches 1

  • 2 years ago

    (x^2 +x -2)/(x^2 -1)

    (x+2)(x-1)/(x+1)(x-1)

    (x+2)/(x+1)

    As x --> 1, this --> 3/2

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  • david
    Lv 7
    2 years ago

    If you want the limit as x approaches infinity, then you are correct

    ... Limit (as x -->infinity) of [X2+x-2/x2-1] = 1

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