find the limit as x->3 of (1-sqrt(x-2))/(x-3)
I'm not sure how to get the answer, I know it's -1/2, but I don'y know how to get that.
lim ( 1 - √(x-2) )/(x-3) as x ---> 3
= lim ( 1 - √(x-2) )/(x-3)*(1 + √(x-2)/(1 + √(x-2) )
= lim ( 1 - (x-2) )/[(x-3)((1 + √(x-2) ]
= lim( 3-x)/[(x-3)((1 + √(x-2) ]
= lim -1/(1 + √(x-2) ) , x ---> 3
= -1/(1 + √1)
= -1/2
If you know Calculus, a quicker way might be to use L'Hopital's rule