Finding a limit as x approaches 0

Can someone please help with this problem? I have a test soon and I don't know how to do these.
Lim as x->0 of

(xtanx-sinx)/x

And also

lim (4-x)/((sqrt of x)-2)
x->4

I multiplied by the conjugate and got zero in the end, but I know that is wrong.

Help please?

1)
(x*tan(x) - sin(x))/x
= tan(x) - sin(x)/x

So the limit is
tan(0) - lim_{x-->0}sin(x)/x
= 0 - 1
= -1

Here I use the fact that lim_{x-->0}sin(x)/x = 1.

2) Multiplying by the conjugate indeed works:

(4-x)/(sqrt(x) - 2)
= [(4-x)(sqrt(x)+2)]/[(sqrt(x) - 2)(sqrt(x)+2)]
= [(4-x)(sqrt(x)+2)]/(x -4)
= -1*(sqrt(x)+2)

So the limit is -1*(sqrt(4) + 2) = -4.