How can values of the function f(x)=cos(2+x) be accurately computed for values of x close to 0?
How can values of the function f(x)=cos(2+x) be accurately computed for values of x close to...
(1) How can values of the function
be computed accurately when x is sufficiently close to 0?
(2) How can values of the function
be computed accurately when x is sufficiently close to 0?
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2. (6 points) Explain why the function f(x) = Vr2+2-1 cannot be computed accurately in a computer when r is large. Then find a way around the problem
9780130130549
3. Near certain values of r each of the following functions cannot be accurately computed using the formula as values of r which are involved (e.g. pose a reformulation of the function (e.g., using Taylor series, rationalization, trigonometric identities, etc.) to remedy the problem. This is problem # 12 from the textbook. Please also see pages 48-49 for examples and more details. given due to cancellation error. Identify the near z 0 or large positive r) and pro- (a)...
Write a function that computes accurately values of f(x) = ^4 squareroot x + 4 - ^4 squareroot x for positive and very large x.
(a) Find all values of a > 0 and BER such that the function cos(ax)-cos(x) for < 0, f(x) = {B for x = 0, In(1+o.r) for x > 0, is continuous at x = 0.
Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0 < x < 3
Question 2-Part B: How many inflection points for the function whose second derivative is f"(x) sin(3x)-cos(x2) for 0
We are the four computed values
of f, IEEE floating point arithmetic is used? You can assume that
exp(x) and exp(-x) are calculated exactly and rounded to the
nearest floating point number
The following lines of MATLAB code evaluate the function 1.5 1016 in four different ways (a) x=1.5e-16; f=0.5*((exp (x)-exp (-x))/x) (b) x -1.5e-16; f - 0.5*((exp(x)-exp(x))/((xt1)-1)) (c) x - 1.5e-16; 0.5* ((exp(x) -exp(-x))/((x-1)+1)) (d) x - 1.5e-16; fexp(x)-exp(-x))/((x+1)+(x-1)) What are the four computed values of f, if IEEE...
Find T5(a): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = T5(x) = Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.001774 of the right answer. Assume for simplicity that we limit ourselves to a < 1. nial of degree 5 of the function f(x) = cos(x) at a = 0.
(2) Consider the function f(x,y) = cos y + sin y (a) Compute the local linearization of f(x,y) at (0,5). (b) Compute the quadratic polynomial for f(x,y) at (0,). (c) Compare the values of the linear and quadratic approximations in part (a) and (b) with the true values for f(,y) at the points (0.007,), (0,0.7924) and (0.7 ). Which approximation gives the closest values ?
2. for the function f(x)= x+2 cos x on the interval
[0,2pi] a. find the first derivative
b.) find the second derivative
c.) find the functions critical values(if any). include their y-
coordinates in your answers in order to form critical points.
d. )find the intervals on which f is increasing or
decreasing.
e. )find the local extrema of f.
f. )find the functions hyper critical values(if any). include their
y coordinates
g.) find the intervals of concavity, i.e. the...