2 Jlju غير مجاب عليه بعد الدرجة من 0 3.0 علم هذا السؤال The Maclaurin polynomial of degree 5 for :the function f(x) = sin(x) is اخترأحد الخيارات x -+ a O 3! 5! 1+2+를 +음bO 3 5! .c - - 3! 1+ x + x? + x³ + x4 + x° .d O
Q: 4. Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial for…
A: To find- Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial…
Q: Find the Taylor polynomial of order 3 centered at 0. 1 f(x) = 5-x x2 O P3(x) = +25 125 625 =-- x x2…
A: Rewrite the function as: fx=15-x =15×11-x/5 =151-x5-1
Q: Interpolate the function f(x) = ev3 on [-1, 1] with a second degree polynomial by using the zeros of…
A:
Q: Let T(x) denote the Chebyshev polynomial of degree k. Express the composite polynomial Tn(Tm(x)) of…
A: The Chebyshev polynomial of first kind defined as Tmx=2xTm-1x-Tm-2x, with initial conditions given…
Q: Let f : R → R be an even 2T-periodic function and let ao, an, bn, for every n > 1, be the Fourier…
A:
Q: Find an expression for the nth Maclaurin polynomial using sigma nota- tion for the function cosh x.
A: Suppose f has n derivatives at x=0 then nth Maclaurin polynomial of f is pn(x) where pn(x)=∑k=0n…
Q: Show that the Chebyshev polynomials have thefollowing properties: Tm(Tn(x)) = Tmn(x)
A:
Q: 4. Use the error formula to find a bound for the error at a = 0.31 in approximating a sin(2x-5+1 on…
A:
Q: Find the Maclaunin polynomial of degree 3 for the fuction. - ge
A: The given function is:fx=e-9xTo find the Maclaurin polynomial.
Q: Let g (x, y) = 9 sin(xy) – 11x² In(y) + 4. Find the degree 2 polynomial, p, which best approximates…
A:
Q: Also, our definition of the first 4 Legendre polynomials is: 1 Po(x) V2 P1 (x) = V5/2 (1 – 312)…
A:
Q: Find the Taylor polynomial T3 for the function f(x) at the numbe sin(9) + cos(9)(x-9). sin (9) +…
A:
Q: 5. Let Tn be the nth Maclaurin polynomial for f(x) = e². Find a value of n suc. le01 – T,(0.1)| <…
A:
Q: 2. Find the Maclaurin polynomials of order n=0,1,2 for f(x) = cos(x).
A: Consider the formula for Maclaurin series: Calculate the derivatives to find the terms in the…
Q: Ax) = eV cos(x) +:
A:
Q: Find ALL irreducible polynomials of degree 2 or 3 in Zr].
A: An irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the…
Q: be Sotve cateulate the thind onderu Tayloru polynomial about (0,0) of Sin(x*+y")
A:
Q: 13 - What is Taylor polynomial with order 3 generated by f(x) = x° + 3x² + 2x + 4 at x = 1.
A: The Taylor polynomial of order 3 is given as follows :
Q: 11. a. For the function f(x) = (3x+2), let x, =-1, x, =0, x, =1. Construct interpolating polynomial…
A:
Q: 2. Find the Maclaurin polynomial of f (x) = cos x.
A: Using maclaurian series of polynomials,
Q: Show that the Maclaurin polynomials for f(x) = sin x are x2n+1 +(-1)"- (2n + 1)! x5 5! T2n+1(x) =…
A:
Q: Let Tn(x) denote the Chebyshev polynomial ofdegree n and defineUn−1(x) = 1/nT'n(x)for n = 1, 2, . .…
A: We have given the equation;
Q: Let p be a polynomial of degree n and let S = { x is an element in interval (0,pi/2) | cos(x) =…
A:
Q: Consider the following. 3x4 - 8x + 5 = 0, [2, 3) (a) Explain how we know that the given equation…
A: Given that 3x4−8x3+5=0, 2,3
Q: Show that the Maclaurin polynomials for f (x) = ln(1 + x) are
A: The given function is fx=ln 1+x. fx=ln 1+x f0=0 f'x=11+x f'0=1 f''x=-11+x2 f''0=-1…
Q: Consider the Taylor polynomial centered at a = 0 with n nonzero terms sin x 2 x - 3! +... 7! 5!…
A: Here we have to match the polynomial with sinx expression.
Q: Use a symbolic differentiation utility to find the Taylor polynomials (centered at zero) of degrees…
A:
Q: (b) Use Taylor polynomial to derive a first order method for approximating f"(zo) that uses f(xo -…
A: The given problem is to find the approximation formula of f"(x0) that uses f(x0-h) , f(x0) ,…
Q: A field is delimited to the north by the streets y= e^x and y= e^-2x, to the south by the street…
A:
Q: :Use a Newton-Gregory polynomial (Forward & Backward) of degree 3 that fit table below, then find…
A:
Q: Determine the third order MacLaurin's polynomial for f(x) = ex.
A: Given, f(x)=ex
Q: Find the second Lagrange înterpolation polynomial that rn tercepts flx)= x²+xe*+sinx at points xo=0,…
A: We have to find the second-order Lagrange interpolation polynomial that interpolates fx=x2+xex+sinx…
Q: Suppose f(2)= 0 anz" is entire. in=0 If |ƒ(z)| ≤ 3|z|ln(|z| + 1) for all z, prove that f is a…
A: Given: fz=∑n=0∞anzn is entire. fz≤3zlnz+1 for all z. To prove: f is a polynomial.
Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…
A: We have to show that, the distinct polynomials x4+x and x2+x in ℤ3x determine the same function…
Q: 2) Let f(x) = lIn(2x) Find 3rd Taylor Polynomial centered at c= 1 for f(x)
A:
Q: Use Taylor's Theorem to find an interval [ — z, z] where the Maclaurin polynomial p2(x) - = 1 1…
A: The given function is fx=cosx and Maclaurin polynomial p2x=1-x22. The Taylor's Theorem states: If…
Q: Explain why the function has at least one zero in the given interval. C f(x) = x² - 4 - cos(x) [0,…
A: Please find attachment below. Where I explain all these things.
Q: Q2 Suppose that f(x) = x* +2x +2 is a polynomial over the field (Z3, +3.3). Is f(x) irreducible over…
A: Just substitute all elements in Z3 in f(x) and check if something is zero.
Q: Example Let f(x) = sin(x). Approximate f() by the Hermite interpo- lating polynomial of degree at…
A: Given the function fx=sinπx To find the value of f14 by Hermite interpolating polynomial when x0=0,…
Q: Find the third order Taylor polynomial of the function f(x)= tanx in powers of (x-1). Select one: 1…
A:
Q: Express p (x) = 1 + 2x - 5x2 as a Taylor polynomial about a=l.
A:
Q: Find the Taylor polynomial of order 3 centered at 0. 1 f(x) = %3D 5-x x3 p3(x) = 25 125 625 x2 p3(x)…
A: Given: fx=15-x The Taylor series of above function when n=3. Taylor series is given by:…
Q: 3. Use a divided difference table to find the Hermite polynomial approximation of a sin(2x-3+1 which…
A:
Q: 2) Find the 3€ Tayler polynomial P,(x) fix) = Sinx at X= -½. 3) Using B,(x) from 2), estimake sin…
A: The formula for taylor series is where f (k) (a) is kth derivative of f at given point a.
Q: Show that the Maclaurin polynomials for f (x) = sin x are x2n+1 T2n+1 (x) = T2n+2 (x) = x – 3!…
A: we have to show that Maclaurin polynomials for f(x)=sinx are…
Q: A scientist has executed one experiment to identify the values of an unknown function f(x). The…
A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…
Q: 6. Find the third degree Maclaurin polynomial for f(x) = cot-(x) and use this to approximate…
A:
Q: Find the degree 2 Taylor polynomial of f(x) = In(x+1) at a = 1. %3D In 2 - -(z – 1) – (2 – 1)? 4 4…
A:
Q: Show that a polynomial p(z) of degree n is orthogonal to any Legendre polynomial PN(z).where N>n,…
A: The Legendre equation is 1-x2y''-2xy'+pp+1y=0 (i) Eq. (i) can be written as…
Step by step
Solved in 2 steps
- A Bitter Dispute With the publication of Ars Magna, a dispute intensified between Jerome Cardan and another mathematician named Niceolo Fontana, otherwise known as Tartaglia. What was the dispute, and how did it arise? In your opinion, who was at fault? Write a paragraph or two about your findings.10 veterans who suffer from PTSD are tested before and after taking an anti-anxiety medication thought to reduce PTSD symptoms. How do I report my findings in APA format? Before condition (M=52, SD= 13.4, SE=4.228) After condition (M=43, SD=13.4, SE=4.243) t(9)=1.581, p >0.05, d=0.500.If the mortality rate under one month infants in a country is 2.5 per thousand, and the same rate for infants up to two months is 6 per thousand: A) What is the approximate mortality rate of 1000 infants in the second month of life? B) What is the probablity that 2500 babies born in that country in one day will reach one month old?
- Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…hw 2 399.1 395 530.7 495.1 476.8 460.9 480.9 450.4 472.7 453.5 446.2 567.3 428.2 547.2 507.8 383 453.5 507.7 506 473.8 392.3 450.7 464.5 403.4 465.8 534.2 471.7 507.7 490.2 481.7 492.4 477.2 507.7 476.8 464.7 390.2 481.7 469 515.7 519.4 396.3 517.2 493.9 515.2 486.5 460.3 475.4 445.5 467.7 531 532.7 486.4 533.8 453.5 Find the first quartile for this data set.Q1 = Find the third quartile for this data set.Q3 = Find the interquartile range for this data set. IQR =Assuming that workers' salaries in your company are uniformly distributed between $30,000 and $90,000 per year. Find the amount of money that 45% of the workers make more than that value?
- in a certain city, 60% of the heads of household own the house in which they reside, and 80% of the heads of the household have full-time employment when considering what percentage of heads of household both own their home and have a full-time job, a student estimates that 48% of heads of household fit both requirements, stating that (0.60) (0.80)=0.48. is this student correct in his approach?To determine the effectiveness of an oil additive, a testing firm purchased two cars of the same make, year, and model, and drove each a distance of 30,000 miles using the same kind of gasoline, the same kind of oil, the same driver, under the same road conditions. The oil in one engine included the additive, whereas the oil in the other engine did not. At the end of the test, the engines of both cars were dismantled, and it was found that the engine that contained the additive had less wear. The testing firm concluded that the oil additive caused the reduced wear.The Department of Mathematics of a certain university in a recent survey was found to consist of 80 faculty members. The survey also revealed the information that among them, there are: 40 male professors; 38 married professors; 26 professors with more than 10 years of service; 15 married male professors; 14 married professors with more than 10 years of service; 13 male professors with more than 10 years of service; and 6 married male professors with more than 10 years of service. How many unmarried female professors have less than or equal to 10 years of service?
- An automobile insurance company classifies applicants by their driving records for the previous three years. Let U = {all applicants}, A = {applicants who have caused accidents}, B = {applicants who have received speeding tickets}, C = {applicants who have been arrested for driving while intoxicated}. Suppose we are given the following information: 3 applicants have caused accidents, received speeding tickets and been arrested for driving while intoxicated. 31 applicants have caused accidents and received speeding tickets. 26 applicants have caused accidents and been arrested for driving while intoxicated. 9 applicants have received speeding tickets and have been arrested for driving while intoxicated. 63 applicantshave caused accidents. 47 applicants have received speeding tickets. 57 applicants have been arrested for driving while intoxicated. There are 120 applicants total. (a)Describe the following set using set theoretic notation: {applicants who have not caused accidents and…Consider a town with a population that is 10 percent black (and the remainder is white). Because blacks are more likely to work the night shifts, 20 percent of all cars driven in that town at night are driven by blacks. One out of every 20 people driving at night is drunk, regardless of race. Persons who are not drunk never swerve their car, but 10 percent of all drunk drivers, regardless of race, swerve their cars. On a typical night, 5,000 cars are observed by the police force. a. What percent of blacks driving at night are driving drunk? What percent of whites driving at night are driving drunk?b. Of the 5,000 cars observed, how many are driven by blacks? How many of these cars are driven by a drunk? Of the 5,000 cars observed at night, how many are driven by whites? How many of these cars are driven by a drunk? What percent of nighttime drunk drivers are black?c. The police chief believes the drunk-driving problem is mainly due to black drunk drivers. He orders his policemen to…People come to relationships with different attachment styles that partially stem from the attachments they experienced with the adults raising them and partially due to experiences in other relationships in their lives. Those who have what is known as “secure” attachments are comfortable with their partners emotions, can help soothe, and make movements towards the other person in a responsive way. Among a group of 10 individuals rated as having a secure attachment style, a researcher wanted to know if, as they were first being acquainted with another person, the amount of self-disclosure made them like their person more. The data is listed in Table 6 below. Test the hypothesis at an alpha of 0.05 (where increasing scores mean higher disclosure and higher liking). If you knew the new person you are about to go on a date with had a self-disclosure rating of 4, what would you predict your likeability score would be (provide the full regression formula as well as the response)? -use…
