Question

Use zero to third order approximations, respectively to
determine *f*(*x*) = (4*x* - 6)^{3}
using base point *x _{i}* = 2 by Taylor series
expansion. Approximate

Answer #1

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Write the Taylor series for the function f(x) = x 3− 10x 2 +6,
using x = 3 as the point of expansion; that is, write a formula for
f(3 + h). Verify your result by bringing x = 3 + h directly into f
(x).

Using the first four non-zero terms of the Taylor series
expansion of 12/x^4 , approximate the value of exp(0.01) and
calculate the error by comparing the obtained value with the actual
value of exp(0.01).

Use Newton’s Method to approximate a critical
number of the function ?(?)=(1/3)?^3−2?+6.
f(x)=1/3x^3−2x+6 near the point ?=1x=1. Find the next two
approximations, ?2 and ?3 using ?1=1. x1=1 as the initial
approximation.

Approximate the zero for f(x) = (x^3)+(4x^2)-3x-8 using newton's
method
Use x1 = -6
A)Find x2,x3,x4,x5,x6
B)Based on the result, you estimate the zero for the function to
be......?
C)Explain why choosing x1 = -3 would have been a bad idea?
D) Are there any other bad ideas that someone could have chosen
for x1?

Consider the function, ? (?) = 19x^4 + 23x^3 - 20x, Use
zero-to-fourth-degree approximation to predict ? (5) using as a
base point ? = 3. Compute the relative true percentage error ?? for
each approximation. Briefly discuss your results, provide a brief
narrative (5 pts.).

Construct the Taylor series of f(x) = sin(x) centered at π.
Determine how many terms are needed to approximate sin(3) within
10^-9. Sum that many terms to make the approximation and compare
with the true (calculator) value of sin(3).

The second-order Taylor polynomial fort he functions
f(x)=x√x about X0= 1 is P2= -1/2+3x/2+3(x-1)^2/8
using the given Taylor polynomial approximate f(1.05) with 2 digits
rounding and the find the relative error of the obtained value
(Note f(0.05=1.0759). write down the answer and all the
calculations steps in the text filed.

The second-order Taylor polynomial fort he functions f(x)=√1+x
about X0= is P2=1+(x/2)-(x^2/2) using the given Taylor polynomial
approximate f(0.05) with 2 digits rounding and the find the
relative error of the obtained value (Note f(0.05=1.0247). write
down the answer and all the calculations steps in the text
filed.

The second-order Taylor polynomial fort he functions f(x)=xlnx
about X0= 1 is P2= -1+(x-1)^2/2 using the given Taylor polynomial
approximate f(1.05) with 2 digits rounding and the find the
relative error of the obtained value (Note f(1.05=0.0512). write
down the answer and all the calculations steps in the text
filed.

4.
Use the “zero” utility of your calculator to determine the zeros of
f(x) = x^2 + 5x - 10 (round to the nearest tenth if necessary).
5. What are the zeros of the polynomial f(x) = x^4 (x-2)^2
(x+1)? Tel whether each zero is odd or even.
7. Use synthetic division to determine if k = -3 is a zero of
f(x) = 2x^3 + 13x ^2 + 30x + 25. Give the answer as “yes” or “no”.
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