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 f( 6)(x) of f(4)(x)= (x2+1)2 Differentiation

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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: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h (x) = sin 2x

A: We have to determine whether the function hx=sin2x is in the span of the functions fx=sin2x and…

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

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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 the finite difference formula for the second derivative at point x=x; with points X₁, Xi+1,…

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Q: f(0) = sec0 is one-to-one on the interval [O,π] with π/2 removed.

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Q: 1. Find the fourth Maclaurin polynomial for f (x)= sin 2x.

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Q: Verify that f′(x) = g′(x) and explain the relationship between f and g

A: fx=3xx+2f'x=ddx3xx+2=x+2(3)-(3x)(1)x+22=3x+6-3xx+22=6x+22

Q: 2. Suppose we are given the following information about a signal x(t): i. x(t) is real and odd. ii.…

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Q: Use the secant method to estimate the root of the f(x) = 3x + sinx - ex llowing brahi function:

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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: Find the interpolating polynomial to the function f (x)= In(x +1)+sinx at x – 0, 1, 2, 3, 4, 5…

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