Question

Evaluate the limit:
lim 25-(x+2)^2 / x-3
x->3

Answer 1

25(x-3) = 25 x -75

so
[ 25 x -75 - x^2 - 4 x - 4 ] /(x-3)

[-x^2 + 21 x -79 ] / (x-3)

(x-3) is not a factor of the numerator so I can not get rid of it in the denominator.
as x goes to 3 the numerator becomes -25 and the denominato is 0 so undefined is the answer.
If you mistyped it and mean
[ 25-(x+2)^2 ]/ (x-3 )
then
[ 25 - x^2 - 4 x - 4 ]/ (x-3)
that is
[ - x^2 - 4 x + 21 ] / (x-3)
- [ x^2 + 4 x - 21 ] / (x-3)
- (x-3)(x+7) / (x-3)
-x - 7
-3 - 7
-10
PLEASE US PARENTHESES SO WE CAN TELL NUMERATOR FROM DENOMINATOR !!!!!

Answer 2

sorry! the question was
lim [25 - (x+2)^2] / [x-3]
x->3

Answer 3

so
-10

Answer 4

I figured you must have mistyped it because (x-3) simply had to be a factor of the numerator or the question would not have been asked.