2.2. For a particular parametric curve, it is found T2) dx (t+2) In(7-t) We note that dy Do an indeterminate analysis and see which of the 4 cases below applies. dx t=-2 dy What to do when (or any of the 7 indeterminate forms) for dxlt=a parametric equations x = x(t), y = y(t) What to do: Evaluate lim ay tea dx This limit will result in four possible cases Case (1). lim-= 0 -> Graph has horizontal tangent line att = a t-a dx Case (2). lim dy -= too -> Graph has vertical tangent line at t = a ten dx Case (3). lim - = c where c is a non-zero real number - Graph has a tangent line at t = a that is neither horizontal nor vertical Case (4). lim - DNE and is not too > Graph does not have tangent line att = a ten dx and may have a sharp corner or be discontinuous 2