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)]
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|
but when , , so: