Question

Find the limit of the function as x approaches 1:

f(x) = (\sqrt{26 - x} - 5) divided by (\sqrt{17 - x} -4)

I would like a hint.

Answer 1

Do we have to do conjugate for this?

Answer 2

Try it and see, yes.

Answer 3

I failed.

Answer 4

I realized that I can take out the radical from the top, but no matter what, the bottom will still output a 0 when subbing in for 1.

Answer 5

I think the simplification you did with the denominator is incorrect.

Answer 6

Oops, yes.

Answer 7

It would be 1-x if you expanded.

Answer 8

So that did not work.

Answer 9

Do you know l'Hopital's rule?

Answer 10

Can't use that at this stage.

Answer 11

Okay, I have this...How about Double rationalization...rationalize them both! Numerator and Denominator.....

Answer 12

Ah, yes. Nicely done.