1. (a) Use Taylor's theorem to find the first-order Taylor series for tan r about r = 7/4 and the associated remainder term. Hence determine whether the integral RT / 4 dx 1 - tan x is convergent or divergent. (b) Suppose that, for t > 0, I (t ) = tan -' ( * ) dx. Use the Leibniz rule to find I'(t). Hence show that, at t = 1, I(t) is positive, increasing and convex