Consider the curve with parametric equation

Consider the curve with parametric equation
x(t) = t + sin t, y(t) = t + 2e
−t
,
where t ∈ [−2, 10].
(a) Find the equation of the tangent at the point (0, 2). Give your result in the
form y = mx + p.
(b) Find the coordinates of the points where the is a vertical tangent, and the
points where there is a horizontal tangent.

2. Find the length of the curve with parametric equation
   x(t) = t
   2
   cost, y(t) = t
   2
   sin t, t ∈ [0, 1].