Verified answer

The top can be rewritten as (3+sqrt[t])(3-sqrt[t]) right? Since the bottom is (3-sqrt[t]), we can cancel those from the top and bottom to get the function 3+sqrt[t]. Evaluate at t=9 to get 3+sqrt[9]=3+3=6, as the book claims. Does this help?

Edit: I'm glad I was able to help....does that mean I get best answer? :)

To answer this question, you need to simplify the fraction so that it no longer gives you 0/0 by factoring and canceling out. In general, you should do this whenever you have some 0/0.

You could do one of the following in order to simplify the fraction:

1) multiply the denominator by its conjugate (3+√t) in order to get rid of the radical in the denominator, then factor and cancel out

2)factor and cancel in terms of √t, making life much easier for all.

either way, the important aspect is that you need to cancel something out.

I will do the second. So, you can rewrite the top in the fraction as follows:

(9 - (√t)^2)/(3 - √t) =

(3 + √t)(3 - √t)/(3 - √t) =

3 + √t

now, if you plug in t = 9, you get

3 + √9 = 3 + 3 = 6.

NOTE: this is not what the function of that point actually is. The answer is undefined because you're not allowed to divide by 0, and when t=9 the denominator is 0. However, for every single other point, you can say that it's the same as 3 + √t and thus state that the LIMIT is 6.

Are you typing this in correctly? Because, I get 3.

9 - 9/3 - 3 = 9 - (3 + 3) = 9 - 6 = 3