Please Answer The Following Questions, show all work please!

1. (4 pts. each) Consider a curve given by the parametric equations: = t+ Int y = t- Int (a) Find an equation of the line tangent to the curve at t = 1. (b) For which values of t is the curve concave up?2. (7 pts.) Find the arc length of the curve: I = tsint = tcost Hint: [ sec3 0do = (sec 0 tan 0 + In |seco + tan #)) + C' 3. (7 pts.) Find the area of the region enclosed by one loop of the curve. Hint: consider r = cos(30)Determine whether the series is convergent or divergent by expressing s, as a telescoping sum (as in Example 8). 27 n(n + 3) n = 1 O convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) X