Consider the plot of a nonlinear function f(x) shown in Fig. 1 i)ii)-2Graphically estimate the linearization function f(x) at the operating point x = 1.Estimate the relative linearization error at x = 1.5 and at x = 2.-121O-1Fig. 1: Nonlinear function f(x)-N-2

We are given a graph. We need to linearize the given graph (an unknown function) at the operating…

Answered: i) ii) -2 Graphically estimate the…

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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3. Find the slope of the curve of the function y at the point P (2, ).
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): X 1= average high school grade in mathematics (HSM) X 2 = average high school grade in science (HSS) X 3 = average high school grade in English (HSE) X 4 = SAT mathematics score (SATM) x 5 = SAT verbal score (SATV) A first-order model was fit to the data with the following results: SOURCE DF MS F VALUE PROB>F MODEL 28.64 5.73 11.69 0001 ERROR 218 106 82 0.49 TOTAL 223 135.46 ROOT MSE DEP MEAN 0.700 R-SQUARE 0.211 4.635 ADJ R-SQ 0.193 PARAMETER STANDARD T FOR O VARIABLE ESTIMATE ERROR PARAMETER -0 PROB> ITI INTERCEPT 2.327 0.039 5.817 0.0001 0.0003 XI HSM) X2 (HSS) X3 (HSE) X4 (SATM) X5 (SATV) 0.146 0.037 3.718 a.036 0.038 0.950 0.3432…
The energy requirements for walking (ƒ(x) in W/kg) were determined for 8 Adélie penguin chicks with respect to walking speed (x in m/s). The relationship can be approximated by the linear function ƒ(x) = 41.3x + 8.9, for speeds between 0 and 0.3 m/s. (a) Approximately what is the energy requirement for walking at a speed of 0.2 m/s?(b) Find and interpret the slope of the line.
Exercise 3. Find and verify the type of stationary points for the following functions: a. f(x) = x² + 4x² - 4x₁ - 8x₂ b. f(x) = x² + 2x² + 4x₁ + 4x₂ c. f(x) = 2x² - 4x² d. f(x) = 2x2-3x² - 6x1x₂(x₂-x₁ - 1) e. f(x) = (x₂-x²)² - x³
2. The point (3, 6) is on the graph of y=3f(x-1)-3. What is the original point on y = f(x)?
Consider the three points (2, 2), (4,4), and (6, —2). (a) Supposed that at (2, 2), we know that fx = fy = 0 and ƒxx 0, function near the point (4,4)? ? fxy fry = 0. What can we conclude about the behavior of this (c) Supposed that at (6, -2), we know that fx = fy = 0 and fxx > 0, fyy < 0, and fxy = 0. What can we conclude about the behavior of this function near the point (6, -2)? ? Using this information, on a separate sheet of paper sketch a possible contour diagram for f.

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i) ii) -2 Graphically estimate the linearization function f(x) at the operating point x = 1. Estimate the relative linearization error at x = 1.5 and at x = 2. -1 2 1- O -1 Fig. 1: Nonlinear function f(x) -N- 2