Question

evaluate without using l'hopitals law

lim x->(1) (((2)-((X+3)^(1/2))/(2X-2))

Answer 1

Rationalize first the numerator of the expression.

Answer 2

how though? do i change the square root to an exponent??? I tried to look up steps to solve but it only shows me hospitals rule but I can't use it as we haven't covered it in class yet and i have to "use only what has been learned to solve"

Answer 3

can i multiply by the conjugate?

Answer 4

yes. :)

Answer 5

so right now i have…
lim x->(1) (x+7)/((2x+2)(2+((x+3)^(1/2)))

Answer 6

i got 1/2 not -1/8 so i did something wrong

Answer 7

Probably, you were misled with 4-(x+3), right? It should be 4-(x+3)=4-x-3=1-x.
Also, the given is (2x-2), not (2x+2).

Answer 8

yeah so now i have lim x-> (1) (1-x)/((2x-2)(2+((x+3)^(1/2))) and I'm stuck cause if i fill in i still get 0 in the denominator

Answer 9

In the numerator, (1-x)=-(x-1). In the denominator, (2x-2)=2(x-1).

Answer 10

I got it!!! Thank you SO MUCH!!!

Answer 11

Your welcome. :)