Exercise 2.1 (a) x(t)=t(2 ?t) ^?1 for t ?[1, 2). (b) for t ?[2, + ?). (c) for . (d) for every t ?[0, 1). (e) x(t)= ? t ln t+2 t for t ?[1, + ?). (f) x(t)=(1 ?t ²)(2 t) ^{? 1} for t ?[1, + ?). (g) x(t)=t(ln t+1) ^?1 for t ?[1, + ?). (h) for t ?[1, + ?). (i) x(t)= te ^t for t ?[1, + ?). (j) x(t)=( t ⁶+11)(6 t ²) ^?1 for t ?[1, + ?). (k) x(t)=(e ^t ?e)t ? ¹ for t ?[1, + ?). (l) x(t)=( t ln t ?1) ^?1 for t ?[1, t*), where t* is the root of the transcendental equation t ln t ?1=0. (m) for t ?[1, e ⁴). (n) x(t)= t ^?1 for t ?[1, + ?). (o) x(t)=(2 t ? t ²) ^?1 for every t ?[1, 2). (p) x is implicitly defined by the equation x ³ ? x ²+ t ²=0 for t ?[1, + ?).

Problem 2.1 One may easily state that the function z