Let (xn) be a bounded sequence, and for each n ∈ n let sn : = sup{xk : k ≥ n} and tn : = inf{xk : k ≥ n}. prove that (sn) and (tn) are monotone and convergent. also prove that if lim sn = lim tn, then (xn) is convergent. [one calls limsn the limit superior of (xn), lim sup xn, and lim tn the limit inferior of (xn), lim inf xn.]

answer: a

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

answer: 8

step-by-step explanation: if you add the possibilities 5 different flavor and 3 different sizes 5+3=8