Answer Happy

What is the EXACT Answer of X1? I don't want a whole bunch of
equations, Thank You.
Bessel functions arise in several important applications. There are several types and several families of Bessel functions - all indexed by integers (or half-integers). Bessel functions of the first kind are denoted by Jn (with JR : [0,00) + R); in Matlab, they are implemented as besselj. They are oscillatory functions with infinitely-many zeros. To see a graph of Jo (2x) try the following in Matlab: fplot(@(x) besselj(0,x),(0,100]) We wish to construct an approximation to the first zero X1 of J. (a) which is located in the interval I = (1, 3). To achieve this, let {bi, i = 1,2,3} denote the set of Chebyshev nodes Pi mapped from (-1, 1) to (1,3). Let p(x) denote the simple Hermite interpolant of Jo (2) at {Xi, i = 1, 2, 3). Find the root of p(x) in I and write down this value (rounded to 5d.p.). Recall that the set of n Chebyshev nodes located in (-1,1) is given by (2i – 1) Pi = cos i=1,2,...,n. 2n You may want to use the identity 16 (2) = -J1(x). -

Use Newton's method to find the exact double precision value of the first zero X1 of Bessel's function of the first kind J. (x) (see previous question), i.e., find X1 so that Jo(X1) = 0 exactly in Matlab (using format long). Enter this value below. X1