I follow what you have done.
However, if that limit is something I should already know, then no, I haven't seen it before. Does it equal 1?
Well it's the slope of the tangent of the curve at the point , that is: the limit of the slope of the secant with one fixed point in and the other point moving towards that fixed point ( ).
Yes, this limit has the value 1.
Well it's the slope of the tangent of the curve at the point , that is: the limit of the slope of the secant with one fixed point in and the other point moving towards that fixed point ( ).
Yes, this limit has the value 1.