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Pistol Pete
Pistol Pete asked in Science & MathematicsMathematics · 1 decade ago

Find limit of equation using f(a+h) - f(a) / h?

f(x)= 2/(x-1).... a=2.

Please show work along with answer.

1 Answer

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  • cidyah
    Lv 7
    1 decade ago
    Favorite Answer

    f(a+h)=2/(a+h-1)

    f(a)=2/(a-1)

    f(a+h)-f(a) = 2/(a+h-1) - 2/(a-1) = [2(a-1)-2(a+h-1)]/(a-1)(a+h-1)

    f(a+h)-f(a) = (2a-2-2a-2h+2) /(a-1)(a+h-1)

    f(a+h)-f(a) = -2h /(a-1)(a+h-1)

    [f(a+h)-f(a)] / h = -2 / (a-1)(a+h-1)

    lim h-->0 [f(a+h)-f(a)] / h = lim h-->0 -2/(a-1)(a+h-1)

    = -2/(a-1)^2

    a=2; the limit is -2/(2-1)^2 = -2

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