# Calculus: limits

posted by .

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)

• Calculus: limits -

Factor (25-t) into (5-sqrt(t)) and (5+sqrt(t))

Cancel top and bottom (5-sqrt(t) and left with lim t->25 of (5+sqrt(t))

which is 10.

• Calculus: limits -

The idea of rationalizing the denominator is excellent.
You may note that the denominator is of the form (A-B), so if you multiply top and bottom by (A+B), you will get (A²-B²) in the denominator.
Since you are taking the limit, t does not equal 25, so you are allowed to divide top and bottom by (25-t). Simplify and get a neat answer in no time.

## Similar Questions

1. ### Math(I Don't Get THIS!!)

15sqrt8x^16/5sqrt2x^4 *I totally need help with this one!Please help me.! I'm going to assume your problem is this: 15√(8x^16) / 5√(2x^4) You can start by simplifying what's outside the square root sign. 15/5 reduces to …
2. ### MATH PLEASE CHECK IT!!2

sqrt2/sqrt10 here is what I got: sqrt (2/10)= sqrt (1/5) sqrt 0.2 * I don't think that it is right but pleasee check it.Thanks Yes, that is one way you could do it, then simplify further by taking the square root of 0.2, but you are …
3. ### Algebra 1

Simplifying Radicals, Use the quotient property to simplify the expression. 3 times the square root of 6/3 3*sqrt(6/3) is the same thing as saying 3*sqrt(2) Your problem: 3√(6/3) is the same as 3√6/√3 To rationalize …
4. ### Algebra

How would i complete these problems? 1. (√6mn)^5 2. ^3√16x - ^3√2x^4 3.^4√x • ^3√2x 4. ^3√72x^8 5. √63a^5b • √27a^6b^4 and are these problems correct?
5. ### Math

Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3x-y=1 and x+y=-2. a. (3√2 +√10)x-(√10 + √2)y-2√10+√2=0 b. (3√2 - √10)x+(√10 - √2)y+2√10+√2=0 …
6. ### Algebra 2 Answer Check

Simplify by rationalizing each denominator. 1. 2/√3 A: 2√3 / 3 2. -18/√6 A: -3√6 Add or subtract. 3. 4√3 - 9√3 A: -5√3 4. √8 - 15√2 A: -13√2 5. √45 + √20 A: 5√5 …