Calculus: limits
posted by Kay on .
Evaluate the limit at t > 25: [25  t] / [5  √(t)]
I multiplied it by √(x + 3) to get rid of the square root on the bottom. However, once I'm done distributing it out, I'm not sure I'm doing it right.
I get [x√(x+3) + 2x  2] / [x + 5]
Once I plug in 25 for t, I get really big numbers and I end up getting an off number that is not correct (like 25√28 + 48 / 30)
Can someone please help?

Factor (25t) into (5sqrt(t)) and (5+sqrt(t))
Cancel top and bottom (5sqrt(t) and left with lim t>25 of (5+sqrt(t))
which is 10. 
The idea of rationalizing the denominator is excellent.
You may note that the denominator is of the form (AB), so if you multiply top and bottom by (A+B), you will get (A²B²) in the denominator.
Since you are taking the limit, t does not equal 25, so you are allowed to divide top and bottom by (25t). Simplify and get a neat answer in no time.