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Math Help - help with this calc problem-limits, continuous function?

  1. #1
    Junior Member LexiRae's Avatar
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    help with this calc problem-limits, continuous function?

    the function f is continuous at t=1
    if f(t) = sqrt (t +3) - sqrt (3t+1)
    all divided by by (t-1) for all values of t not equal to 1, and f(t) = k when t =1, what is k?
    i know you have to find the limit of f(t) as t approaches 1. but im not sure how?
    THANKS! lexi
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by LexiRae View Post
    the function f is continuous at t=1
    if f(t) = sqrt (t +3) - sqrt (3t+1)
    all divided by by (t-1) for all values of t not equal to 1, and f(t) = k when t =1, what is k?
    i know you have to find the limit of f(t) as t approaches 1. but im not sure how?
    THANKS! lexi
    begin by multiplying by the conjugate of the numerator over itself, that is, do

    \lim_{t \to 1} \frac {\sqrt{t + 3} - \sqrt{3t + 1}}{t - 1} \cdot \frac {\sqrt{t + 3} + \sqrt{3t + 1}}{\sqrt{t + 3} + \sqrt{3t + 1}} = k
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