A. Use brackets to make you question clear, otherwise we are just guessing

what you question realy is.

B. I will assume you mean for your first question:

lim as theta-->pi/4 tan[theta (sin(theta))^2)]

Or:

Now as is continuouse at the limit may be evaluated by just plugging into this to get:

C. By " lim x-->5 from the left 3x-15/|x-5|" I will assume you mean:

lim x-->5 from the left (3x-15)/|x-5|

or:

but when , , so:

RonL