Use the second Taylor polynomial P2(x) for f(x) = r? + cos(x) about co = 0 and evaluate S f(x)dx.

Q: Let f(x)= cos 2x-(x- 2) a) Find the 3rd Taylor polynomial about xo= 0.5 b) Using this polynomial…

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Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

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Q: For which value of x does the Maclaurin polynomial Tn satisfy Tn(x) = f (x), no matter what f is?

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Q: If x >= 0 and y >= 0, prove that √xy <= (x+y)/2.

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Q: Determine the order of the zero at the origin of f(x) = ² (cos(z) - 1 + sin² (2))

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Q: the error estimate for Taylor polyno

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Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…

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Q: Find the absolute maximum and minimum of f(t) = -2cos2t + sin4t on  the interval [0,pi/4]

A: The given function is, f(t)=-2cos2t+sin4t and the given interval is, 0,π4. Obtain the value of the…

Q: - Find the extrema of the function (x)= 5 sin(2x) - 2x - 4x - Using Newton's method - Using…

A: Consider the equation

Q: Let f(x) = sinx and x, = 0, x1= 0.5, xX2 = 0.7.Construct the second Lagrange polynomial for f(x) to…

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Q: Let f(x) = x'/3. By using quadratic Lagrange interpolating polynomial for the given function f(x)…

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Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: Find the intervals in which the function f(x)=sin (log,x)+cos(log,x)is decreasing.

A: By the first derivative test, a function is decreasing if its derivative is less than zero.

Q: X Let F(x) = ²* sin(6t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). Use this polynomial…

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Q: Let P, (x) be the Legendre polynomial of degree n. Show that for any function, f(x), for which the…

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Q: Let g (x, y) = 7 sin(xy) — 9x² ln(y) + 8. Find the degree 2 polynomial, p, which best approximates g…

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Q: Find the integration distance (f, g) = √² f(x)g(a) da between the given polynomials. f(x) = -4x-1,…

A: Step 1: Step 2: Step 3: Step 4:

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Construct a Langrange Interpolating polynomial of…

A: The given question is solved below

Q: Find the integration distance (f, g) = | f(x)g(x) dx between the given polynomials. f(x) = -5x + 1,…

A: Given that  (f,g)=integral f(x)g(x)dx  To find the integration distance

Q: Consider the following functions: (i) z = arctan (-) -(√) (ii) z= In (iii) z = (ex-ex) sin y. Which…

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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: B. Find a root of the function f(x)=x²-x-cosx by using Fixed point method (Do five iteration and…

A: Given equation is…

Q: Show that the function f(x)= x^3 − 15 cos(pi x) + 1 has three zeros in the interval [−4, 4]. Do not…

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Q: Find the third ordered polynomial for approximating f(x) = cos(x) centered at a = pi/3.

A: We Use the Taylor's series, Find the ordered polynomial for approximation Given Function and Given…

Q: Consider the following three functions: f(t) = sin((t-2)), g(t) = ㅠ sin ·(t — 4)), 31 ) =…

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