Forest (x 2-2x+1)/(x 2-1) = lim (x-1)/(x+1) = 0.

2

lim[(x+h)^2-x^2]/h=lim(2hx+h^2)/h=2x

three

lim(x^2- 1)/(2x^2-x- 1)=lim(x- 1)/(2x+ 1)

= lim( 1- 1/x)/(2+ 1/x)= 1/2

four

lim(x^2+x)/(x^4-3x^2+ 1)

=lim( 1/x^2+ 1/x^3)/( 1-3/x^2+ 1/x^4)

=0

five

lim(x^2-6x+8)/(x^2-5x+4)=lim(x-2)/(x- 1)=2/3

six

lim[( 1+n- 1)*(n- 1)/2]/n^2

=( 1/2)lim(n^2-n)/n^2

=( 1/2)lim( 1- 1/n)/ 1

=( 1/2)

seven

lim( 1+ 1/n)( 1+2/n)( 1+3/n)/5

= 1/5

eight

The topic is unclear.

nine

lim w*(sinwx/wx)=w

lim 3*(tan3x/3x)=3

lim(2/5)(sin2x/2x)/(sin5x/5x)= 2/5

lim(x/sinx)cosx = lim cosx/(sinx/x)= 1

lim2sinx^2/xsinx=lim2(sinx/x)=2