Posted by **Labiba** on Saturday, February 25, 2012 at 11:58am.

Evaluate the limit:

lim 25-(x+2)^2 / x-3

x->3

- Calculus -
**Damon**, Saturday, February 25, 2012 at 12:15pm
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 !!!!!

- Calculus -
**Labiba**, Saturday, February 25, 2012 at 12:19pm
sorry! the question was

lim [25 - (x+2)^2] / [x-3]

x->3

- Calculus -
**Damon**, Saturday, February 25, 2012 at 12:22pm
so

-10

- Calculus -
**Damon**, Saturday, February 25, 2012 at 12:23pm
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.

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