How can we know if the limits to these actually exist and if they do, what are they.

1) lim (x---->0) {(sqrt(1+2x)) - (sqrt(1-3x))}/{x}

2) lim (x---->1) {3(x^4) - 8(x^3) + 5}/{(x^3) - (x^2) -x -1}

3) lim (x----->infinity) {(sqrt((x^2) +1) - (sqrt((x^2) -1)}