Hello, i need help with calculus

\fFor each set of conditions below, give an example of sequencesIseries that satisfy the conditions (and show that they do), or explain why the sequence/series cannot exist. (a) A sequence {an} that is not monotonic, but converges to the limit 2021. (b) A series 2 an that can be shown to converge using the Integral Test, but not the Ratio Test. 00 00 00 (c) Two different series 2 an and 2 15,, that converge to the same sum, and another series 2 an that diverges, 11:1 13:1 12:1 such that an 5 an 5 5,, for all n. Consider the following curves 01I$3+y3:1 OEI$3+y3:9 03zy:m+1 C4zy:0 that are shown in the figure below. Dene the following regions, also shown in the gure above. - Q is the region bounded by 03 on the left, Cl on the right, and C4 below. - R is the region enclosed by all four curves: above 01 and 04, below 03 and 02. (a) Use a Riemann Sum to approximate the area of the region Q. Use any rule we studied in class, and n : 4 subintervals. (b) Set up integral(s) to compute the area of the region R. (c) Set up integral(s) to compute the volume of the solid obtained by rotating Q around 04