1. Evaluate: lim x->0 (sqrt((x+4)-2)/x

2. Show that the limit of 4x-1 as x->2 is 7.

1. lim ( √(x+4) - 2)/x , as x-->0

=lim ( √(x+4) - 2)/x * ( √(x+4) + 2)/( √(x+4) + 2)
= lim (x+4 - 4)/(x(√(x+4) + 2)
= lim 1/( √(x+4) + 2) , x --> 0
= 1/(2+2) = 1/4

#2.
In any limit question, the first thing I do is to sub the approach value into the expression.
If I get a real number, that is my answer, all done
so....
lim (4x-1) , as x --> 2
= 4(2) - 1
= 7