Question

Find the limit of the function algebraically.

limit as x approaches five of quantity x squared minus twenty five divided by quantity x minus five.

Answer 1

\[\lim_{x \rightarrow 5} \frac{ x^2-25 }{ x-5 }\]

Answer 2

Well if we put a 5 in that equation we get 0/0, so we should look for stuff that we can factor out.

You might have noticed that the numerator is a difference of squares.

Answer 3

formula for difference of squares
\[a^2-b^2=(a-b)(a+b)\]
so can you apply that to the numerator?

Answer 4

Yes but they need to do it algebraically, so not using L'Hopital's rule

Answer 5

so how do i get the answer

Answer 6

We need to get rid of that x-5 in the denominator because when we plug in x=5 we get a 0 in the denominator...

So do what I said above and use the difference of squares on the numerator.