Use Taylor's Theorem to find an interval [−z,z][-z,z] where the Maclaurin polynomial p3(x)=x−x^3/6 approximates f(x)=sin(x) to within 1/6    [−z,z]=?

Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

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Q: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

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Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = 1

A: The given functions are, f(x)=sin2x, g(x)=cos2x, h(x)=1. To Check: Whether the function h(x)=1 is in…

Q: Find all the analytic functions for ReZ=Im f(z)

A: Find all the analytic functions for ReZ=Im f(z)

Q: (@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

A: To explain why the given function is entire, given function is: fz=5z4−6+zcosz−z3ez

Q: Obtain a quadratic polynomial approximation to f (x)= 3e* using Newton divided difference…

A: Given:        f(x)=3ex       Here h=b-aN                  =0.5-04=0.125     The value of table for x…

Q: Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer…

A: The given functions, 1. y=tanx6 2. y=x5+9 3. y=e7x We have to write the functions in composite form…

Q: Prove the identity. Work on one side only. cos(4x) = 18 sin² x+8 sin ¹ x

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Q: Prove that dl = (Vu) x (Vv) - do.

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Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then,…

A: The truncation error is of order O∆x3 The step length are ∆x, -∆x

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: 3 prove that sinh (2) isine

A: Since you have posted multiple questions, we will provide the  solution   only to the first question…

Q: Find the analystic function f(z)u+iv if u=a(1+cos0)

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Q: Use/Bisection]Method to find the root of f(x)= x' - x e– 2 = 0, that lies in the interval (2,3) for…

A: The bisection method performs iterations on the midpoint of an interval to approximate the root of…

Q: f(t) = mt + b+ A sin-

A: Given data:     The given price of the model is: f(t)=mt+b+Asin(πt/6). The given price on the first…

Q: Prove that the function n = x(x^2 - 3y ^2)+ (x^2 - y^2) + 2xy is harmonic. Also find the conjugate…

A: Then,     and Thus,   and , it follows  that .Hence, the  given function is harmonic.(Proved)…