27. A function on [0,2] defined by-x²5x - 44x³ - 3x(3x + 4if x ≤ 0if 0 < x≤ 11

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Answered: 27. A function on [0,2] defined by f(x)…

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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25. (LO12) For the function f (x) = (x – 1)² + 2, state the intervals over which this function is increasing, decreasing, or remaining constant. A) Increasing: (1, ∞); Decreasing: (-0, 1); Constant: none B) Increasing: (2, 0); Decreasing: (-, 2); Constant: none C) Increasing: (-1, *); Decreasing: (-00, -1); Constant: none D) Increasing: (1, 0); Decreasing: (2, 0); Constant: none
Suppose that the functions fand g are defined as follows. f(x) = -5x² +1 g (x) = Vx+3 Find f-g and f· g. Then, give their domains using interval notation. (f- 2)(+) = 0 G (0,0) (0,0) Domain of f - g :0 OvO (0,0) (0,0) 00 -00 (*3)(;) = 0 ? Domain of f g
Find the discontinuities of the function 2х — 1 - if 2 < x x +1 1 Let G be the function defined by G(x) = if – 1< x < 2 - - -3 if x < -1 | 2.
How do you solve question 1,2 and 3?
5. Discuss the continuity of the function x²-1 f (x) = x+- 1 at x = -1. *+2 2, x=- 1
How large should n be to guarantee that the Trapezoidal Rule approximation to x - 12x- 48x² + 2x + 5) dæ is accurate to within 0.1. n = How large should n be to guarantee that the Simpsons Rule approximation to 2 1(-a - 12a - 48z? + 2x + 5) dx is accurate to within 0.1. n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n Question Help: Video 1 D Video 2 Submit Question P Type here to search hp
5. Is the given function continuous at x-3? Justify your answer. Also decide, Is the function continuous for all real numbers x ? g(x) = (x² + 2x - 33, x² - 6x +9 x-3 if x ≤ 3 if x > 3

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27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ - 3x (3x + 4 if x ≤ 0 if 0 < x≤ 1 1