11. Here we consider two functions that are defined in termsof the floor and ceiling functions.(a) Let f(n) = [] + [3] for n € N. Calculate f(n)for 0 ≤ n ≤ 10 and for n = 73.(b) Let g(n) = [] [] for n e Z. g is the charac-teristic function of some subset of Z. What is thesubset?

11. (a) Given, f(n)=n2+n3 for n∈ℕ.

Answered: 11. Here we consider two functions that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The number of U.S. farms with milk cows can be modeled as f(x) = 45.183(0.831x) + 60 thousand farms where x is the number of years since 2000, based on data for years between 2001 and 2007 (a) Were the number of farms with milk cows increasing or decreasing between 2001 and 2007? a) increasing b) decreasing (b) What is the concavity of the function on the interval 1 ≤ x ≤ 7? a) concave up B) concave down
Page of 2 5. The following piece-wise function summarizes the tax levied by the United States government on the adjusted gross income earned by a head of household in 2020. if x 311,025 (0.10x | 1,413.00 + 0.12(x-9.900) 6.159.00 + 0.22(x- 53,700) { 13,164.00 + 0.24(x - 85,550) 31.824.00 + 0.32(x - 163,300) 45.920.00 + 0.35(x- 207.350) 82,206.25 + 0.37(x - 311.025) T = Calculate the income tax levied by the United States government on a head of household taxpayer in 2020 on a taxable income of a. $195.900. b. $28,050.
3. (a) From the graph of f, state the numbers at which f is discontinuous and explain why. (b) For each of the numbers stated in part (a), determine whether f is continuous from the right, or from the left, or neither. + -4 -2 YA 0 + 2 4 6 X
Please show me the solution step by step
Find the domain of the function, and then determine for each of the indicated interval whether the function is continuous on that interval.
2.22. Let f be a function from R to R. Without using words of negation, write the meaning of "f is not an increasing function".
4.1.2
1. From the graph of g, state the intervals on which g is continuous. -7 -5 i. ني f(x)=- ii. _f(x) = 0 1 2 x²-1 x+1 2. Explain why the function is discontinuous at the given number a. 1 (x-1)² ,a=1 3 ,a=-1 5 7 X
consider the graph of the function f on the interval [-3,3] below

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11. Here we consider two functions that are defined in terms of the floor and ceiling functions. (a) Let f(n) = []+[] for ne N. Calculate f(n) for 0≤ n ≤ 10 and for n = 73. (b) Let g(n) = []-[] for n e Z. g is the charac- teristic function of some subset of Z. What is the