5. Given the following polynomials: P(x)=32(x+1)+0(x + 1)(x) + (x + 1)(x)(x - 1) and Q(x) = −1 +4(x+2) - 3(x+2)(x + 1) + (x+2)(x+1)(x) == (a) Show that P(x) and Q(x) both interpolate the data Ꮖ f(x) | - -2 - -1 0 2 -1 3 1 - -1 3 (b) Why does part (a) not violate the uniqueness property of interpolating polynomials?

5. Given the following polynomials: P(x)=32(x+1)+0(x + 1)(x) + (x + 1)(x)(x - 1) and Q(x) = −1 +4(x+2) - 3(x+2)(x + 1) + (x+2)(x+1)(x) == (a) Show that P(x) and Q(x) both interpolate the data Ꮖ f(x) | - -2 - -1 0 2 -1 3 1 - -1 3 (b) Why does part (a) not violate the uniqueness property of interpolating polynomials?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Simplify the following two Boolean functions using K-MAP:c) F(A, B, X, D) = ∑ (2, 3, 10, 11, 12, 13, 14, 15) d) F(A, B, C, D) = ∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)
Given the following function: f(x) = 2x For g(x) = Sf(x) dx, determine g(x).
1. Consider the following functions of n. (1) (2) (3) (4) (5) (6) (7) (8) (9) fi(n) = n, if n = 2.k for k = 0, 1, 2,... = n², otherwise. f2(n) = n, if n = 3.k for k= 0, 1, 2,... = n², otherwise. f3(n) = log n. Answer the following questions and prove your answ Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. fi(n) = 2(f₂(n)), f2(n) = Q(fi(n)), fi(n) = 0 (f₂(n)), f₂(n) = 0 (fi(n)), fi(n) = O(n), f₂(n) = O(n²), f3(n) = O(√n), f3(n) = O(fi(n)), 22n = 0(2¹), swer for each one.
Q2 Find the minimum expression for each of these functions. (a) f(A, B, C) = M₁ + M3 + M4 +m6 (b) f(d,e,f) = Σm(1,4,5,7) (c) f(r, s, t) = r't' + rs' + rs (d) f(a, b, c) = M3 + M₁ +M6 + m₂ m(2,3,5,7) (e) f(n, p, q) =
The Lagrange polynomial that passes through the 3 data points is given by x 15 18 22 y 24 37 25 f2(x)=L0(x)(24)+L1(x)(37)+L2(x)(25) The Value of L1(x) at x = 16 is ???
The solution is using Matlab
Q3 Find the minimum sum-of-products expressions for each of the following functions (d denotes don't care terms). (a) f(A, B, C, D) = Σm(4,11,12,13,14) + Σm(5,6,7,8,9,10) (b) f(A, B, C, D) = Σm(3,11,12,13,14) + Σm(5,6,7,8,9,10) (c) f(A, B, C, D) = m(1,2,4,13,14) + Σm(5,6,7,8,9,10) (d) f(A, B, C, D) = Σm(4,15) + Σd (5,6,7,8,9,10)
Simplify the following functions using K-maps, and then derive the corresponding simplified Boolean expressions. Note that d stands for don't-care cases. a) F(w,x,y,z) = Σ(0,2,8,10, 12, 13, 14) b) F(w,x,y,z) = (0,2,3,5, 7, 8, 10, 11, 14, 15) c) F(A,B,C,D) = [[(1,3,6,9,11,12,14) d) F(x,y,z) = (0,4,5,6) and d (x, y, z) = Σ(2,3,7)
Simplify the following Boolean function F, together with the don’t-care conditions d, and then express the simplified function in sum-of-minterms form: F(A,B,C,D)= ∑(2,4,10,12,14) d(A,B,C,D)= ∑(0,1,5,8)
F(A, B, C, D) = Σm(0, 1, 2, 3, 9, 10, 13, 14)G(A, B, C, D) = Σm(0, 1, 8, 9, 10, 12, 13, 14)H = AD′ + A′B′C + ABC Using the functions from the previous section, encode F, G, and H using the following PLA. Youwill need to share terms between functions. Label each line with its product term
1. Apply Bisection method to find the root (only one root) of the function: f(x) = 8sin(x) + 8cos(x) fromthe bracket -10 to 10.0. Use only 10 iterations and give the value of the rootSample answer is given below: