F(x) = Sin JC 1. Determine the first 3 non-Zero Taylor polynomial OF FEXS = Sin xc about the point terms of the 2. 2. What is the degree of the polynomial determined in the previous as question

Q: 3. Let d 2 2 and let P(z) = ao + ajz + ... + a4z“, ad # 0 be a polynomial with real coefficients…

A: Please note that I am able to see only one part, namely part (a). So, I can solve only part (a) for…

Q: find taylor degree of polynominal at degree of 4 at c is pi/4 for f(x): sin(x)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Determine the stepsize that can be used in the tabu- lation of f (x) = sin x in the interval [0,…

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Q: The function below has two roots between x = -6 and x = 10. Use the bisection method to estimate the…

A: Given: The function has two roots between  x = -6  &   x=10, And the function is  fx=x+53 -ex…

Q: Hind the cooffecPents + ax tb=0, where c = 3 anod x =-2 are tha roots a anod b f1om the oquatfon,

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Q: Express f(x)= 4+ 6 x² + 7 x + 2 in terms of Legendre Polynomials.

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Q: Determine the 3rd degree Maclaurin polynomial for f (x)= cot"(x) cot"EI) then use this to estimate…

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Q: What are all the roots of f(x) = x* – 3x³ +x – 32 A -1, 3 only 1 ti3 only 2 1tiV3 -1, 3, 2 1, -3, VI…

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Q: LOW: Construct polynomia -) sinx in [0, 2π] interpolation in mentioned interval of the function

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: (-1)" Given: In(1+ x) Σ if |a| < 1. n + 1 n=0 3. Use the third degree Maclaurin polynomial of f to…

A: Third degree polynomial

Q: Using Newton's interpolating polynomial of order 2, namely, bo +b,(x-x)+b,(x-x)(*-x) where x, = 0,…

A: Given:   Newton’s method for polynomial interpolation of order two is given as:…

Q: 8. What are all the roots of the function f(x) = (x² + 1)(x – 2)? ? 2. -1 and 2 iand 2

A: solve for x over the real numbers (x^2+1)(x-2)^2=0 Split into two equations  (x-2)^2=0 or (x^2+1)=0…

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

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Q: Let f(x) =xe*. a) Find the third Taylor polynomial P(x) for the function f(x) about x; = 0. Use this…

A: Note: As per Bartleby's guidelines, for more than one question asked in the main part, only one…

Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: Find the formula for the fourth degree polynomial containing the point (0,8) and whose graph is…

A: We have to find the equation for the given graph.

Q: Start with p =-1.5 and p, =-1.52 and use the secant method to find the root p=-1521of the polynomial…

A: p0 = -1.5 p1 = -1.52 f(x) = x3 - x + 2

Q: Find the rational roots of x* + 8x + 7x-40x- 60= 0. 02,6 О-6, -2 O-2, 6 О-6, 2

A: Given  x4+8x3+7x2-40x-60=0 let, f(x)=x4+8x3+7x2-40x-60 Given that there is at least one and possibly…

Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

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Q: Find a polynomial function with real coefficients that has the given zeros. (There are many correct…

A: Given the zeros of a polynomial function 58,−1,7+5i

Q: Use the Newton's Divided Difference formula to compute the cubic interpolating polynomial for f(x) =…

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Q: 5. a) Find the second Taylor's polynomial P2(x) approximating the function f(x) = x + In (1+ x)…

A: Consider the given function. fx=x+ln1+x (a) We have to find the second-order Taylor polynomial about…

Q: 3- Use the bisection method to find a root of the equation x² = -sin x in the interval [-1, 0] with…

A: Solution: The equation is x2=-sinx Rewrite it as x2+sinx=0 Let fx=x2+sinx Interval is -1,0

Q: Consider the function f(x) = cosa, -, . Construct the Lagrange interpolation polynomial which…

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Q: Q5) Find the root of f(x)= 5 sin(x) + ex² by using bisection method take a= -1.25 and b= -1.0 for…

A: Given, fx=5sinx+ex2. Here, a=-1.25b=-1.0 Now,…

Q: Use Bisection method to find the root of f(x) = x2-3. Use the initial guess of XL = 1 and LU = 2.…

A:

Q: 2) Given: f(x) = (x-1) (x+ 1) was transformed to (x) = (x- 1)(x+ 1)-1. How many roots would the…

A: f(x)=(x-1)2(x+1)2 was transformed to f(x)=(x-1)2(x+1)2-1.

Q: 9. Estimate the error in approximating sin(0.5) by using the fifth-degree Maclaurin polynomial by…

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Q: Let p(x) be a polynomial function of degree n with simple roots r1,..., xn. Show that ) p"(x;) = 0.…

A: Let Pn be a given statement for all natural numbers n. If  i. P1 is true ii. Pk+1 is true whenever…

Q: Let f be the Taylor polynomial P,(x) of order 7 for tan¹ x about x = 0. Then it follows that, if…

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Q: +∞ x sin(x2) : = - Σ n=0 (-1)" .4n+3 (2n + 1)! X

A: Let's find 7th degree maclaurin polynomial.