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

1. ## 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

2. Originally Posted by LexiRae
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

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