Thread: Limit Defintion of the Derivative/ Rationalization help

I have the function f(x)= the square root of(x+2). i must find the limit of x=2 as h approaches zero. When i rationalize the numerator in the problem i get (4h-4)/(2h times the square root of (h) +2h). I do not see anyway to simplify the problem. Can anyone see what im doing wrong/ not doing?

Originally Posted by gamefreeze

I have the function f(x)= the square root of(x+2). i must find the limit of x=2 as h approaches zero. When i rationalize the numerator in the problem i get (4h-4)/(2h times the square root of (h) +2h). I do not see anyway to simplify the problem. Can anyone see what im doing wrong/ not doing?

Now you want to multiply by the conjugate of the numerator to get

thank you very much. So it is easier to not input the values of x until i am done simplifying?

Originally Posted by gamefreeze

thank you very much. So it is easier to not input the values of x until i am done simplifying?

It is a matter of opinion. I personally think so, but it can go either way. The reason I like to do it last is because it is more general, the formula is valid for any x, not just x=2.

ok thanks a lot
when not plugging in the values of x, the algebra is much easier to do.