(d) Evaluate the following limits (i) lim x(ex- 1) xe* (iii) lim (ii) lim dt t+1 sin2 5x y-0 y (iv) lim + 4 k=1 (e) Use an appropriate local linear approximation to estimate V9. (f) Prove that the function F(x) = dt 1+t dt 1+t2 is constant on the interval (0,+co).