Homework Answers
The degree of f is 3
and the degree of f' is 2.
From the polynomial's curve we can observe the turning points or
bumps in the graph and the flex point:
In the given f curve, we have 2 bumps and 1 flex, thus degree =
3:
So, in general, the number of turning points/bumps and the flex points are equivalent to the degree of the polynomial and it's differential (i.e. f') will be one degree less.
Upvote, if the answer was helpful. Have a nice and safe day.
Add Answer to:
4. Using your knowledge of the shapes of polynomials, what degree polynomial is f? What de-...
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f...
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
4. Let f()VI+ x. (a) Compute P2(x), the degree 2 Taylor polynomial for f at ro...
4. Let f()VI+ x. (a) Compute P2(x), the degree 2 Taylor polynomial for f at ro 0. (b) Use P2 to approximate f(0.5) required to evaluate a real polynomial of degree 5. How many multiplications number? Explain n at a real are 6. Show that if x, y and ry are real mumbers in the range of our floating point system, then ay-f(ry3 + O(*) ay
Determine whether the function is a polynomial function. If it is, identify the degree. F(x) =...
Determine whether the function is a polynomial function. If it is, identify the degree. F(x) = 2x2 + 5** Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It is a polynomial. The degree of the polynomial is B. It is not a polynomial > ary Ons Click to select and enter your answers) and then click Check Answer All parts showing CA Copyright 2020 Pearson Education Inc. All rights reserved....
Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x+50)4/3 at a=2 Find the second-degree Taylor polynomial for f(x)=4x2−7x+6 about x=0 thank you
Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(7x+50)4/3 at a=2Find the second-degree Taylor polynomial for f(x)=4x2−7x+6 about x=0thank you! (:
1,2,3, and 4 Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f an...
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Find a polynomial f(x) of degree 4 that has the following zeros. 2, 0, 7, -6...
Find a polynomial f(x) of degree 4 that has the following zeros. 2, 0, 7, -6 Leave your answer in factored form f(x)-Ф
Part A-Multiple Choice K/U-20 marks] 1. If the leading coefficient of an odd-degree polynomial function is...
Part A-Multiple Choice K/U-20 marks] 1. If the leading coefficient of an odd-degree polynomial function is positive, then the function extends from the third quadrant to the first quadrant; that is, as * , y -co and as →-co, y → b. * →-co, y → and as x 0, y →-60 * →-co, y →-co and as x 0, y → d. X-CO, y -co and as x, y →-00 a. c. c. c. 6 2. Which polynomial function...
3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred...
3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred at x = 1. Do this in two ways: (a) Use the general formula at the top of page 60--calculating successive derivatives of vx. (b) Change variable so you can directly use the formula of Ex 4.6: 1 17 1/ 11315 (1 + y)1/2 = 1+3y + 2 + - 41 2 y4 + ... ull- 2 2 2 Now we ask how accurate...
1a): Find the roots of the following polynomial equations using matlab: f(x) = x^5 − 9x^4...
1a): Find the roots of the following polynomial equations using matlab: f(x) = x^5 − 9x^4 + 31x^3 − 51x^2 + 40x − 12 f(x) = x^5 − 11x^4 + 47x^3 − 97x^2 + 96x − 36 b): Find the coefficients of two polynomial equations in matlab given the following sets of roots: r1 = [ 100 25 50 5 10 ] r2 = [ 11 22 33 0 55 ] c): Create a figure with four subplots, each showing...
Problem 5. Consider least squares polynomial approximation to f(x) = cos (nx) on x E [-1,1] using...
Problem 5. Consider least squares polynomial approximation to f(x) = cos (nx) on x E [-1,1] using the inner product 1. In finding coefficients you will need to compute the integral By symmetry, an 0 for odd n, so we need only consider even n. (a) Make a change of variables and use appropriate identities to transform the integral for a to cos (Bcos 8)cos (ne) de (b) The Bessel function of even order, (x), can be defined by the...
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
4. Let f()VI+ x. (a) Compute P2(x), the degree 2 Taylor polynomial for f at ro 0. (b) Use P2 to approximate f(0.5) required to evaluate a real polynomial of degree 5. How many multiplications number? Explain n at a real are 6. Show that if x, y and ry are real mumbers in the range of our floating point system, then ay-f(ry3 + O(*) ay
Determine whether the function is a polynomial function. If it is, identify the degree. F(x) = 2x2 + 5** Choose the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It is a polynomial. The degree of the polynomial is B. It is not a polynomial > ary Ons Click to select and enter your answers) and then click Check Answer All parts showing CA Copyright 2020 Pearson Education Inc. All rights reserved....
1,2,3, and 4
Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Find a polynomial f(x) of degree 4 that has the following zeros. 2, 0, 7, -6 Leave your answer in factored form f(x)-Ф
Part A-Multiple Choice K/U-20 marks] 1. If the leading coefficient of an odd-degree polynomial function is positive, then the function extends from the third quadrant to the first quadrant; that is, as * , y -co and as →-co, y → b. * →-co, y → and as x 0, y →-60 * →-co, y →-co and as x 0, y → d. X-CO, y -co and as x, y →-00 a. c. c. c. 6 2. Which polynomial function...
3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred at x = 1. Do this in two ways: (a) Use the general formula at the top of page 60--calculating successive derivatives of vx. (b) Change variable so you can directly use the formula of Ex 4.6: 1 17 1/ 11315 (1 + y)1/2 = 1+3y + 2 + - 41 2 y4 + ... ull- 2 2 2 Now we ask how accurate...
Problem 5. Consider least squares polynomial approximation to f(x) = cos (nx) on x E [-1,1] using the inner product 1. In finding coefficients you will need to compute the integral By symmetry, an 0 for odd n, so we need only consider even n. (a) Make a change of variables and use appropriate identities to transform the integral for a to cos (Bcos 8)cos (ne) de (b) The Bessel function of even order, (x), can be defined by the...
Most questions answered within 3 hours.
-
John needs 40 Eternal Light flashlights. Each Eternal Light
flashlight requires 3 bulbs, and each bulb...
asked 1 minute from now -
1) If Nominal GDP is $16,000 billion and the GDP deflator is 50,
then Real GDP...
asked 4 minutes ago -
D. A student completed 20 courses in the School of Arts and
Sciences. Her grades in...
asked 1 hour ago -
teo
pucks moving on a frictionless air table are about to collide. the
1.5 kg puck...
asked 1 hour ago -
Problem #1
The area between Z = 0 and Z = 2.50
The area between Z...
asked 3 hours ago -
1. What is the meaning of the term communication style?
2. What are the benefits to...
asked 2 hours ago -
9.) You are buying a car that cost $26,500. You make payments of
$412 each month...
asked 3 hours ago -
. Suppose a discrete random variable has probability
distribution
P(x) = .2 if x = 0...
asked 4 hours ago -
Under the influence of its drive force, a snowmobile is moving
at a constant velocity along...
asked 5 hours ago -
Why do organizations decline? What steps can top
management take to halt, decline, and restore organizational...
asked 4 hours ago -
What mechanisms Drive speciation??
(I.e. what was Dawins theory on the orgin of species, and how...
asked 6 hours ago -
The manager at a car assembly plant believes that the mean
assembly time for a car...
asked 7 hours ago