Tan(pi/4 +h)-1/h. how do i find this as the limit of h approaches 0.?

Two ways come to mind.

The first involves simply invoking the definition of the derivative at a point. If it exists, then it's equal to



where . This means the limit in question is given by



i.e. the derivative of at . We have



so the value of the limit is



The other way to go about this is with trig identities. I seem to always forget the sum identity for tangent, but that's easily derivable if you know the corresponding (co)sine identities.




Now,

Yes, two vertical lines can be complementary