1) The following set of five problems is based on the parametric equations below x(t) = lit 40511) 7? ya) = 'I =cos t (a) [5 pts] Find the values of parameter t {if any) on the interval [0, 21:] such that the slope of tangent to the parametric curve is 1/2. If no such tangent exists, you need to explain the reason. [Hint Use trigonometric identities to get a quadratic equation in sin 1: or cos it from the derivatives and solve for L] . . :12 . . . (h) [5 pts] Find the expression for {13; usmg the above parametric equations and evaluate the second derivative at t = E. (c) [5 pts] Find the area bounded by the curve represented by the parametric equations above . . TI 3:: and the x axls on the Interval 3,? of parameter values. (d) [5 pts] Find the arc-length ofthe curve represented by the parametric equations above on HRH the interval [3,? of parameter values. Evaluate the integral numerically with four equal subintervals of parameter values; use trapezoidal rule. (e) [5 pts] Find the curved surface a es: of the solid generated when the curve represented by the parametric equations above is re JOlVEEl around the x axis. Evaluate the integral numerically with four equal subintervals of parameter values; use Simpson's rule