(a) Show that the equation ecos() - x3 = sin(x2) has a solution in the interval [0, ]

comprises.

(b) Prove or disprove the following statement:

Let (an)n>1 be an arbitrary sequence and (bn)n>1 be a zero sequence. Then also (at bn)n>1 is a Zero

sequence.

(c) Give an example of the following statement: An unbounded sequence can be a con-

have a hidden partial sequence.