Use the known values of the function sin(x) at x = 0, π/6, π/4, π/3, and π/2 to derive an interpolating polynomial p(x). What is the degree of your polynomial? What is the interpolation error magnitude |p(1.2) − sin(1.2)|

Q: plot the function f(x)=x*sin(x)-cos(x) to show that it has one root at the interval [0,pi/2]

A: The given function is  defined in the closed interval .We shall fill the following tabular column.…

Q: How do you know that the functions sin x, ln x, and ex are not polynomials? Give reasons for your…

A: Polynomials have finite terms. And it has a highest degree.  But sinx , lnx and ex have infinite…

Q: (2) Let f(x) = -3 sin(x+2). (c) And then determine the domain and range of f(x).

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Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: Use appropriate Lagrange interpolating polynomials to approximate f(1) if f(0) = 0, f(2) = −1, f(3)…

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Q: ) Define the domain and range of f(x) where f(x) = sin²(x) – 1

A: The function f(x)=sin^2(x)−1 is defined for all real numbers x because the sine function, sin(x), is…

Q: t f(x) be a function tabulated over 4 points, as shown in the table below. Using a degree 3 Newton…

A: Introduction: Extrapolation is the process of computing the value of a function outside the given…

Q: f(x) = tan¬1(2x²) – 1

A: Newton's Raphson Method:- Hence Positive root of given equation by NRM is 0.88244

Q: (c) Show that f(x)>0 for all values of x, x # -2.

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Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π.    Find the intervals of increase and…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.  Find the intervals of increase and…

Q: Find the definition set of the following function F(x)= √ln(sinπx)

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Q: find concavity and inflection point?  f(x)=x2 (8-x2)1/2

A: Find the derivative of f(x).

Q: (b) Construct the Lagrange polynomial. y=sir interpolation. the for function y=sinak taking points…

A:

Q: The (picture1) table is given for the function f(x) = ln x. a) Construct the Newton Divided…

A: The calculations with steps and the approximated polynomial are given in the below steps.

Q: 1. Differentiate the following functions a. f(x) = sin(x) cos(x)

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Using the x coordinates, -2, -1.5, 0, 3, 3.5, 4, find the interpolating polynomial that fits the…

A: Given x coordinates -2, -1.5, 0, 3, 3.5, 4. The objective is to find the interpolating polynomial…

Q: Find the anditerivative of the function f with the given condition f(x) = 0.528 - 4.5 sin(6.5x) and…

A: To find the anti-derivative of the function  with the given condition. and

Q: Consider the functions: f(x) = (cos(x) − sin(x))/cos(2x) and g(x) = 1/(cos(x) + sin(x)) where in…

A: cos(2x) = cos^2(x) - sin^2(x)

Q: Let ƒ(x) = 4x − sin(4x). a) Find f (0). f(0) = b) Find ƒ(§). ƒ(§) = CHECK ANSWER

A: Given query is to find the value of the function at indicated points.