sketch the graoh of the polynomial function f using trchniques
described in this section. f(x)=x2 (x2-4)...
sketch the graoh of the polynomial function f using trchniques
described in this section. f(x)=x2 (x2-4) (x+2)
Solutions
Expert Solution
The question refers to some techniques described in some section
which are missing here. So we have solved the problem based on our
knowledge. Please find the attachments and the graph of the given
function below:
a) For the function f (x) = x – exp(−x2), do a calculation by
hand using a calculator to find the root to an accuracy of 0.1. At
most, five iterations (or fewer) are needed to obtain the desired
accuracy.
b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of
Newton’s method (by hand); tabulate the result.
Draw a quick but accurate sketch of f(x) = √x2−4 over
the interval [−4,0]. This covers the interval of integration.
Partition the interval of integration into 10 intervals. Show
this on your graph with a right or left Riemann Sum
Create a table showing your interval index, i, the value
xi at which you evaluate f(x) in each interval, the
values of f(xi) and ∆x for each interval, and the
contribution each rectangle makes toward the Riemann Sum. Evaluate
the...
The function described by f(x) = ln(x2 + 1) − e0.4x cos πx has
an infinite number of zeros.
(a) Determine, within 10−6, the only negative zero.
please don't use any program while solving it, thanks.
Let f(x) = 1 + x − x2 +ex-1.
(a) Find the second Taylor polynomial T2(x) for f(x)
based at b = 1.
b) Find (and justify) an error bound for |f(x) − T2(x)| on the
interval
[0.9, 1.1]. The f(x) - T2(x) is absolute value.
Please answer both questions cause it will be hard to post them
separately.
Using the function f(x)=ln(1+x)
a. Find the 8 degree taylor polynomial centered at 0 and
simplify.
b. using your 8th degree taylor polynomial and taylors
inequality, find the magnitude of the maximum possible error on
[0,0.1]
c.approximate ln(1.1) using your 8th degree taylor polynomial.
what is the actual error? is it smaller than your estimated
error?Round answer to enough decimal places so you can
determine.
d. create a plot of the function f(x)=ln(1+x) along with your
taylor polynomial. Based on...
A quadratic function f is given.
f(x) = x2 + 6x + 8
(a) Express f in standard form.
f(x)
=
(b) Find the vertex and x- and y-intercepts of
f. (If an answer does not exist, enter DNE.)
vertex
(x, y)
=
x-intercepts
(x, y)
=
(smaller x-value)
(x, y)
=
(larger x-value)
y-intercept
(x, y)
=
(d) Find the domain and range of f. (Enter your answers
using interval notation.)
domain
range
A particle is described by the wave function ψ(x) =
b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤
-a and x ≥ a, where a and b are positive real
constants.
(a) Using the normalization condition, find b in terms of
a.
(b) What is the probability to find the particle at x =
0.21a in a small interval of width 0.01a?
(c) What is the probability for the particle to be found between x...
A particle is described by the wave function ψ(x) = b(a2 - x2)
for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are
positive real constants.
(a) Using the normalization condition, find b in terms of a.
(b) What is the probability to find the particle at x = 0.33a in
a small interval of width 0.01a?
(c) What is the probability for the particle to be found...
2. For the function : f(x) = x2 − 30x − 2
a) State where f is increasing and where f is
decreasing
b) Identify any local maximum or local minimum values.
c) Describe where f is concave up or concave down d) Identify any
points of inflection (in coordinate form)
3. For the function f (x)= x4 − 50 2
a) Find the intervals where f is increasing and where f
is decreasing.
b) Find any local extrema and...