verify whether the characteristic function of X + Y is equal to the product of the characteristic functions of X and Y.

Q: Consider the function ?(?) =1/x and the data points ( 0.1, 10), (0.2, 5), (0.3,3.33) Find Lagrange…

A: Introduction: The formula of Lagrange interpolation polynomial is given by,…

Q: 1. O A. 4 +0+ ヤ+LXA 3 x² 1 O B. (x? + 4) /2 - 4x² + 4 +0 312

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Q: 51+* + 1 y = 5*

A: Given: y=51+x+15x     ⇒   y=51+x5x + 15x                =5+ 15x       y-5=15x           5x=1y-5   x…

Q: don't understand why the -x disappears for the left side of the product rule procedure for the…

A: f(x) = xlnx -x Here the product rule applied on the term (x lnx) only. f'(x) = d/dx (xlnx) + d/dx…

Q: What is Taylor’s polynomial?

A: We know that an nth degree polynomial has the form Px=a0+a1x+a2x2+a3x3+……+anxn where ai's are…

Q: Use appropriate Lagrange interpolating polynomial to approximate f(8.2) , if f(8.3) = 17.56,f(8.1) =…

A: The value of the table for x and y: x 8.3 8.1 8.6 y 17.56 16.94 18.51 We will approximate…

Q: Describe differences between (fog)(x) and (gof)(x). Give examples

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Q: Two similar, but different ones. Consider the function f(x)=exp(x). Let p in P, be the interpolation…

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Q: Derive a 2nd order accurate finite difference expression for the first derivative at point i-1,…

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Q: Based on the definition of divided difference, show that f[x1,x2,x3] = f[x2,x1,x3

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Q: Explain how the Intermediate Value Theorem (IVT) can be used

A: Intermediate value theorem is stated as follows. Consider an interval I=a,b of real numbers ℝ and a…

Q: 1 Compute and simplify the difference quotient for f(x) = V1- x

A: The given function is fx=11-x. Replace x by x+h and obtain that, fx+h=11-x+h. Obtain the difference…

Q: Find the function f(x) = interpolating the data {(0,2), (1, 1)}. %3D z+6

A: A detailed solution is given below.

Q: what should n be if f(x) = Xn defineof a polynomial function?

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Q: ABCD is a square of side a. A line parallel to the diagonal BD at a distance x from the vertex A…

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Q: 4 8.

A: Please see the answer below.

Q: Show that lGl =20 , so G is not simple

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Q: given that the instantaneous rate of change of a polynomial is never zero on the entire domain of…

A: Instantaneous rate of change of a function is nothing but the slope of tangent of a function.If…

Q: x = 1,2,3 f(x) = 4,5, 9 Interpolate a polynomial by using above data with lagrange inerpolation

A: The given data is  x 1 2 3 fx 4 5 9 We have to find the interpolation of a polynomial by…