How can you define these functions at x = 5?

Question

1. (sqrt(x+4) - 3)/(x-5)

2. (sqrt(x+4) - 3)/(sqrt(x-5))

I've started out by multiplying both functions by the conjugate of (sqrt(x+4)+3) but I still have the problem of having (x-5) on the bottom which gives me an answer of undefined.

How do I get rid of (x-5)?

Answer 1

1. multiply both numerator and denominator by sqrt(x+4)+3. You get: numerator=x+4-9=x-5
denominator=(x-5)*(sqrt(x+4)+3).

So, your function becomes:1/(sqrt(x+4)+3). At x=5, you get
f(5)=1/6;

2.use the same principle, but this time, multiply both numerator and denominator by sqrt(x-5) first.

Answer 2

One way to solve these is to take the derivative of the the top and bottom parts. For #1, you should get 0.5 / sqrt(x+4). Set x = 5, and you get 0.166666....

For #2, you get (x-5) / (x+4) = 0 / 9 = 0

Answer 3

yea you can't get rid of x-5, thats the way the function is defined

Answer 4

You can´t as lim x==>5+ is infinity