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Math Help - limit problem

  1. #1
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    limit problem

    lim [f(x) - 8] / [x - 1] = 10
    x ~> 1

    What is the limit as x approaches 1 of f(x)?
    (Hint: let g(x) = [f(x) - 8] / [x - 1])

    i'm not sure how the hint helps me in solving this problem. all i did was multiply both sides of the equation [f(x) - 8] / [x - 1] = 10 by (x - 1) and then added 8 to solve for f(x). then i got f(x) = 10x - 2 and i found that the limit of f(x) as x approaches 1 = 8.

    is this the correct method of doing the problem?

    in case it looked confusing up there, it should read: "the limit as x approaches 1 of (f(x) - 8) / (x - 1) equals 10."
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by oblixps View Post
    lim [f(x) - 8] / [x - 1] = 10
    x ~> 1

    What is the limit as x approaches 1 of f(x)?
    (Hint: let g(x) = [f(x) - 8] / [x - 1])

    i'm not sure how the hint helps me in solving this problem. all i did was multiply both sides of the equation [f(x) - 8] / [x - 1] = 10 by (x - 1) and then added 8 to solve for f(x). then i got f(x) = 10x - 2 and i found that the limit of f(x) as x approaches 1 = 8.

    is this the correct method of doing the problem?

    in case it looked confusing up there, it should read: "the limit as x approaches 1 of (f(x) - 8) / (x - 1) equals 10."
    If you let g(x)=\frac{f(x)-8}{x-1}, we have f(x)=g(x)(x-1)+8.

    Therefore, \lim_{x\to1}f(x)=\lim_{x\to1}g(x)(x-1)+8=0+8=8.

    Does this make sense?
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