Quote:
Originally posted by Locke
Lim->9 (9-t)/(3- square root of t) Do I have to rationalize the denominator first? I've tried rationalizing both the numerator and the denominator) and I just get some strange stuff. Thanks.
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I'll deal with your first question, first, although I don't see how it's an exercise in calculus. It's more like an exercise in algebra but it's good to practice that as well.
I'm not sure what you mean by "rationalizing".
You're probably supposed to note that the numerator is a
difference of squares, so...
Code:
(9 - t) = (3 + sqrt(t))(3 - sqrt(t))
...which means that your equation simplifies like so...
Code:
lim t->9 (9-t)/(3-sqrt(t)) = lim t->9 (3+sqrt(t))(3-sqrt(t)) / (3-sqrt(t))
= lim t->9 3+sqrt(t)
...which should be really simple now. The lim t->9 3+sqrt(t) = 3 + sqrt(9) = 6.
So, the answer is 6...