f(n) = Θ (g(n)) means there are positive constants c1, c2, and k, such that 0 ≤ c1g(n) ≤ f(n) ≤ c2g(n) for all n ≥ n0. The values of c1, c2, and k must be fixed for the function f and must not depend on n. (n^3 / 1000) - 100n^2 + 100n + 3 = Θ(n^3) 1) (n^3 / 1000) - 100n^2 + 100n + 3 <= c(n^3) Let's assume c = 2/1000 (n^3 / 1000) - 100n^2 + 100n + 3 <= 2/1000(n^3) - 100n^2 + 100n + 3 <= 1/1000(n^3) - 100n^2 + 100n + 3 <= 1/1000(n^3) is true for all n >= 0 2) (n^3 / 1000) - 100n^2 + 100n + 3 >= c(n^3) Let's assume c = 1/2000 (n^3 / 1000) - 100n^2 + 100n + 3 >= 1/2000(n^3) (n^3 / 2000) - 100n^2 + 100n + 3 >= 0 (n^3 / 2000) - 100n^2 + 100n + 3 >= 0 is true for some positive value so, (n^3 / 1000) - 100n^2 + 100n + 3 = Θ(n^3)
Problem 1. Express the function 100-100n2+100n+3 in terms of e notation. Completely justify your answer
MA-119 Review for Final Exam: Fall 2019 Simplify completely and express in terms of positive exponents 2. Find the slope interest form of the equation of the line that is perpendicular toy passes through the point. 51 ) 3. Find the slope-intercept form of the equation of the line through the points (-2) and (2 4. Solve for x and check the solution 3x+2 -1 -6 5. Factor completely: a) 12 -10-1815 b)x+ 5x-16x - 30 Based on the graph...
Express x and y in terms of trigonometric ratios of e. (Express your answer in terms of 8 only.) X = y = 32 y Need Hain? ett
< Homework#6 Problem 6.106 Determine the constant a Express your answer in terms of some or all of the variables Ms Ltu Iy, le, and Iy* Consider the general case of a prismatic beam subjected to bending- moment components MyandMs as shown, when the , g, z axes pass through the centroid of the cross section (Figure 1). If the material is linear- elastic, the normal stress in the beam is a linear function of position such that σ =...
1: Solve the following inequalities and express your answer in interval notation. (10 points) x? - 5x-620 Solution 1: 2: Solve the absolute value inequality; 3 - 2x > 9. Write the solution in interval notation. (10 points) Solution 2: (5 points each) 3: For the following function, 3x + 4 f(x)= x+2 3.1: State the domain of the function, Solution 3.1: 3.2: Find x- and y-intercepts (if any), Solution 3.2: 4: Given f(x)=x+5x+2, evaluate the following expression: f(x+h)-f(x) +0....
Extension Questions 21. Are the terms exothermic and exergonic synonymous? Justify your answer with examples. Life cannot exist in a completely closed system (no energy or matter comes into or out of the system) 22. a. Explain why this is true based on the Second Law of Thermodynamics. b. The planet Earth is not a closed system. Ultimately, what is the source of all energy for life on Earth? 23. Consider a process where the increase in entropy of the...
(1 point) Find the domain of the function 1 write your answer in interval notation. Domain: Help: Click here for help entering intervals. You have 3 attempt(s) remaining before you will receive a new version of this problem.
Problem 1: Find the Fourier series for the following function Plot the series using 10 terms, 20 terms and 100 terms Problem 1: Find the Fourier series for the following function Plot the series using 10 terms, 20 terms and 100 terms
The questions for the calculusIII Instructions. Answer each question completely: justify your answers. This assignment is due at 5pm on Wednesday September 25 in Assignment Box #20. 1. Determine if the series given below are convergent. If convergent, calculate the sum of the series. If divergent, justify your answer. 1+23 2 32n n=1 (b) Žlcos(1) (1) § (12 + 3n+3) Suggestion: Use partial fractions. 2. Express this number as a ratio of integers: 2.46 = 2.46464646.. 3. The Fibonacci sequence...
Please write clear in the explanation thanks 1 2 0 -1 3 2 1 -1 2 1 oand RREF(A)- 1 3 -1 2 Suppose that A3 21 a. s there a unique solution to Ax-22 Justify your reasoning completely ?Justify your reasoning completely. b. Are the column vectors of A a basis for R? Justify your reasoning. c. Define geometrically the span of A. 1 2 0 -1 3 2 1 -1 2 1 oand RREF(A)- 1 3 -1 2...
3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution and upper and/or lower bounds, when necessary. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as O(n*) or O(nk log2 n) whenever possible. If the algorithm is exponential just give exponential lower bounds c) T(n) T(n-4) cn, T(0) c' d) T(n) 3T(n/3) c, T() c' e) T(n) T(n-1)T(n-4)clog2n, T(0) c' 3. Determine the...